What can we say about the integral $\int_{\Omega}(f\circ\frac{du}{dt})dt$ in some given conditions on the functions?

Question

If $f:\mathbb R \to \mathbb R$ is a convex function and $u:\Omega \to \mathbb R$ is $C^1$ such that $u|_{\partial \Omega}=0$, where $\Omega$ is a bounded open subset of $\mathbb R.$ Then can we say anything about the integral $\int_{\Omega}(f\circ\frac{du}{dt})dt$ ?

Actually, I need this integral as $0$. Is this possible?

Thank you for your time.