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This page is in need of serious revision. Someone who isn't already familiar with integral calculus would find this section extremely opaque. Someone with a solid understanding of calculus should come in and explain, in clearer language, the geometric meaning behind the integral and provide a picture of a Riemann sum. I can't do everything here.--Mathoreilly 13:40, 2 July 2008 (EDT)

I am going to make some serious changes to this page. The definition of the Riemann integral does not even make sense as it is written. I'll post something in a few days.