Integration by Parts/Primitive

Theorem
Let $f$ and $g$ be real functions which are continuous on the closed interval $\closedint a b$.

Let $f$ and $g$ have primitives $F$ and $G$ respectively on $\closedint a b$.

Then:
 * $\displaystyle \int \map f t \map G t \rd t = \map F t \map G t - \int \map F t \map g t \rd t$

on $\closedint a b$.