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I am trying to run the notebook for a maximum (upper) integration calculation (hopefully, symbolically).

I am using the notebook available at Wolfram Math World (upper left of web page).

When I trying running the code and single example, I am getting all sorts of errors (too many to list). However, the first two errors are the likely culprits and are:

 Get::noopen: Cannot open Utilities`FilterOptions`. >>

 Needs::nocont: Context Utilities`FilterOptions` was not created when Needs was evaluated. >>

How can the

BeginPackage["RiemannSum`", {"Utilities`FilterOptions`"}]

FilterOptions issue be resolved?

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As Compatibility/tutorial/Utilities/FilterOptions says:

The functionality of FilterOptions is provided by the kernel function FilterRules.

Although the syntax is not identical. You have to change two things in the code:

BeginPackage["RiemannSum`", {"Utilities`FilterOptions`"}] 

to

BeginPackage["RiemannSum`"]

And

Begin["Private`"]

to

Begin["`Private`"];
FilterOptions[s_, r___] := Sequence @@ FilterRules[Flatten[{r}], Options[s]];

And it seems to work:

RiemannSumPlot[x^4 - 3 x^2 + 1, {x, -1, 1.9, 29},  ShowEstimate -> False, AxesOrigin -> {Automatic, 1}]

enter image description here

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