diff --git a/packages/squiggle-lang/src/rescript/FunctionRegistry/Library/FR_Danger.res b/packages/squiggle-lang/src/rescript/FunctionRegistry/Library/FR_Danger.res
index 9cbb0710..6e4419a6 100644
--- a/packages/squiggle-lang/src/rescript/FunctionRegistry/Library/FR_Danger.res
+++ b/packages/squiggle-lang/src/rescript/FunctionRegistry/Library/FR_Danger.res
@@ -108,8 +108,8 @@ module Internals = {
       }
       result
     }
-    let xsLength = Js.Math.ceil((max -. min) /. increment)
-    let xs = Belt.Array.makeBy(xsLength + 1, i => min +. Belt_Float.fromInt(i) *. increment)
+    let xsLength = Js.Math.floor((max -. min) /. increment) // Note that we are loosing a bit of the tail
+    let xs = Belt.Array.makeBy(xsLength, i => min +. (Belt_Float.fromInt(i) +. 0.5) *. increment)
     // makeBy goes from 0 to (n-1): <https://rescript-lang.org/docs/manual/latest/api/belt/array#makeby>
     let ysOptions = Belt.Array.map(xs, x => applyFunctionAtFloatToFloatOption(x))
     let okYs = E.A.R.filterOk(ysOptions)
@@ -149,21 +149,48 @@ module Internals = {
       }
       result
     }
-    let xsLengthCandidate = Belt.Float.toInt(Js.Math.round(numIntervals))
-    let xsLength = xsLengthCandidate > 0 ? xsLengthCandidate : 1
-    let increment = (max -. min) /. Belt.Int.toFloat(xsLength)
-    let xs = Belt.Array.makeBy(xsLength + 1, i => min +. Belt_Float.fromInt(i) *. increment)
-    // makeBy goes from 0 to (n-1): <https://rescript-lang.org/docs/manual/latest/api/belt/array#makeby>
-    let ysOptions = Belt.Array.map(xs, x => applyFunctionAtFloatToFloatOption(x))
+    // worked example in comments below, assuming min=0, max = 10
+    let numTotalPoints = Belt.Float.toInt(numIntervals)
+    let numInnerPoints = numTotalPoints - 2 
+    let numOuterPoints = 2 
+    let totalWeight = (max -. min)
+    let weightForAnInnerPoint = totalWeight/.E.I.toFloat(numTotalPoints-1)
+    let weightForAnOuterPoint = totalWeight/.E.I.toFloat(numTotalPoints-1)/. 2.0
+    let innerPointIncrement = (max -. min) /. E.I.toFloat(numTotalPoints -1)
+    let innerXs = Belt.Array.makeBy(numInnerPoints, i => min +. Belt_Float.fromInt(i + 1) *. innerPointIncrement)
+    // Note that makeBy goes from 0 to (n-1): <https://rescript-lang.org/docs/manual/latest/api/belt/array#makeby>
+    let ysOptions = Belt.Array.map(innerXs, x => applyFunctionAtFloatToFloatOption(x))
     let okYs = E.A.R.filterOk(ysOptions)
+
+    // Logging
+    // assuming min = 0, max = 10, results below:
+    Js.Console.log2("numTotalPoints", numTotalPoints) // 5
+    Js.Console.log2("numInnerPoints", numInnerPoints) // 3
+    Js.Console.log2("numOuterPoints", numOuterPoints) // always 2
+    Js.Console.log2("totalWeight", totalWeight)  // 10 - 0 = 10
+    Js.Console.log2("weightForAnInnerPoint", weightForAnInnerPoint) // 10/4 = 2.5
+    Js.Console.log2("weightForAnOuterPoint", weightForAnOuterPoint) // 10/4/2 = 1.25
+    Js.Console.log2("weightForAnInnerPoint * numInnerPoints + weightForAnOuterPoint * numOuterPoints", weightForAnInnerPoint *. E.I.toFloat(numInnerPoints) +. weightForAnOuterPoint *. E.I.toFloat(numOuterPoints)) // should be 10
+    Js.Console.log2("sum of weights == totalWeight", (weightForAnInnerPoint *. E.I.toFloat(numInnerPoints) +. weightForAnOuterPoint *. E.I.toFloat(numOuterPoints)) == totalWeight ) // true
+    Js.Console.log2("innerPointIncrement", innerPointIncrement) // (10-0)/4 = 2.5
+    Js.Console.log2("innerXs", innerXs) // 2.5, 5, 7.5
+    Js.Console.log2("ysOptions", ysOptions)
+    Js.Console.log2("okYs", okYs)
+
     let result = switch E.A.length(ysOptions) == E.A.length(okYs) {
     | true => {
-        let numericIntermediate = okYs->E.A.reduce(0.0, (a, b) => a +. b)
-        let numericIntermediate2 = numericIntermediate *. increment
-        let resultWrapped =
-          numericIntermediate2->ReducerInterface_InternalExpressionValue.IEvNumber->Ok
-        resultWrapped
+        let innerPointsSum = okYs->E.A.reduce(0.0, (a, b) => a +. b)
+        let resultWithOuterPoints = switch(applyFunctionAtFloatToFloatOption(min), applyFunctionAtFloatToFloatOption(max)){
+          | (Ok(yMin), Ok(yMax)) => {
+              let result = ((yMin +. yMax)*.weightForAnOuterPoint +. innerPointsSum*.weightForAnInnerPoint)
+              let wrappedResult = result -> ReducerInterface_InternalExpressionValue.IEvNumber -> Ok
+              wrappedResult
+            }
+          | (Error(b), _) => Error(b)
+          | (_, Error(b)) => Error(b)
       }
+      resultWithOuterPoints
+    }
     | false => Error("Integration error in Danger.integrate")
     }
     result