The main aim of the felxiriemann package is to produce all the different kinds of sums that can be associated with the graph of a real valued function of one real valued variable.
The following pages demonstrate what it can do. I will eventually publish a user guide, but the package file itself has comprehensive instructions for use near the top of the file as comments.
You can download the .sty package file here.
This is version 0.3. It has a much improved function for calculating the average function value on a given interval. This uses a Riemann Sum to calculate the average and then a two stage search to zoom in on the associated x value.
You can download the .tex file that performs the demo here.