Using Mathematica to Estimate Area under a curve

Hey all,

My math professor informed us at the beginning of the quarter that if we could make a program in Mathematica that would help perform a calculation that we've learned how to do by hand in class, he might toss some extra points our way.

I figured that I'd wow him by making a "program" that could display values of the following in a table:

Area using Left, Right, and Midpoints as well as the Trapezoid rule

The function I chose is f(x) = e^(-x^2) (from 0 to 1) and I figured that I'd estimate using 4, 8, 16, 32, and 64 rectangles.

And seeing as how we just talked about error percentages for these, I figured I'd also make a table that displayed their respective errors. (I found the actual value of the area to be 0.746824)

I followed all the command examples that I could find in the help page to create the code for it, but nothing is giving me a concrete answer, and half of the code is giving me an error message (nothing in particular)

Anyone have any pointers on the actual code commands I should be using to accomplish this?

-B