The second fundamental theorem of calculus states that:

If f is integrable in [a, b] and f = g' for some function g, then

$\displaystyle \int_a^b\! f(x) \, dx = g(b) - g(a)$

-----------------------

so I was wondering if there is a function such that it is not Riemann integrable ( $\displaystyle \exists \epsilon, U(f,P) - L(f,P) \geq \epsilon$, or equivalent formulations), and f = g' for some function g.