If h(x)=dg(x)/dx is integrable on the closed interval [a,b], then the integral from a to b of g(x)h(x)dx = ? and it must be in terms of f, g, a, and b
note that if $\displaystyle h(x) = \frac d{dx}g(x)$, then $\displaystyle \int h(x)~dx = g(x) + C$
Thus, using integration by parts, taking $\displaystyle u = g(x)$ and $\displaystyle dv = h(x)$, we have:
$\displaystyle \int_a^b g(x)h(x)~dx = \left. g(x)g(x) \right|_a^b - \int_a^b g'(x)g(x)~dx$
i leave the rest to you