antiderivative of $\psi'(u)$ for $u\in W^{1,2}_0((a,b))$

Question

Let $u\in W^{1,2}_0((a,b))$ and $\psi'$ the derivative of a convex function $\Psi\in C^1(\mathbb{R})$. If I want to consider the antiderivative of $\psi'(u)$, what happens with the $u$ inside $\Psi(u)$? Is it possible to say how does the antiderivative looks like? I need this for an other proof. Regards