From Sean Bird's website: "Put this [TI-Nspire] file in MyLib so that you can access the area approximation methods from any document."
The program will find the approximate areas for the left, right and midpt Reimann sums, as well as the trapezoid, Simpsons and numeric integral areas.
http://cs3.covenantchristian.org/bird/TTT/NspireCalc/area.tns

For other TI-Nspire files from Sean's website, visit:
http://cs3.covenantchristian.org/bird/Nspire.html