Makes sense. Archimedes developed a method of computing areas under a curve by dividing the area into a bunch of rectangles. Of course this is only an approximation, depending on how you draw the rectangles, the actual area is slightly more or less than the sum of the rectangles. http://www.squarecirclez.com/blog/riemann-sums/4715

OTOH, if you take the width of each rectangle to be an very small, and then perform the sum, the error is arbitrarily small, approaching zero in the (infinitesimal) limit.