then we basically have a bunch of rectangles. when n approaches infinity, the rectangles width gets infinity small, and the values for f(x) over that interval pretty much become equal, they differ very little. so we can multiple f(x) by the differential dx, the very small width, and get the anti derivtive of each one of the rectangles. the sum then becomes of a bunch of rectangles, and is now the following. [F(n)-F(n-1)] + [F(n-1) - F(n-2)] ...-[F(2) - F(1)]. THEN, the amazing part....####[]