(First, I'm very sorry if this is in the wrong forum -- I'm taking a general "history of math" class, but I haven't taken any analysis/topology so I'm not sure if this question fits in.)
Anyway, my question is: Take 3 parallel planes with a solid having bases on the top and bottom planes, each base being a simple closed curve. If the second plane moves and the area of the solid intersecting that plane is f(x), graphing f(x) and splitting into small segments of dx=h/n, find a sufficient condition for "for every epsilon, there exists some such that n , V1 - V2 < epsilon.
I know that V1 is the sum of circumscribed rectangles under the curve and V2 is inscribed. Unfortunately I know little else. I'd really appreciate any help.