First note that the Lebesgue-Riemann theorem states that $f:[a,b]\to \mathbb R$ is Riemann integrable if, and only if, $f$ is bounded and is continuous almost everywhere (if a function is not bounded, it can't be Riemann integrable). 

A proof of the more general result for multivariable functions can be found in volume 1 of "Real Analysis" by Duistermaat. A better exercise in fact will be to take this wiki proof and adapt it to $\mathbb R^n$. 

Riemann-Lebesgue equivalence for n-dimensional integration
Newbie question.

Why is it that there's a bazillion different types of screws? Why can't we just always use one standard screw type? Are there advantages/disadvantages to the different types? Are there times when one type is preferred over another?

Help me understand why there isn't one screw to rule them all.
