Excuse me if this is a silly question, but this has never been proven to me and I cannot at the moment see a way to prove this to myself.
So the question is, Are integrals unique, beyond an integration constant? That is, is it true that if
$\int f(x)dx = F(x) + c$ and $\int f(x)dx = G(x) +c $
Then we have $F(x) = G(x)$, for all $x$?