Looking for a method to maximize an integral

Question

I need a method to find a positive real valued function $x(t)$ that maximizes the following integral:

$$ \int_{0}^{+\infty} f\left(\frac{dx}{dt},t\right)\;dt $$ such that $x(0)=0$, $\lim_{t\to \infty}x(t)=N$ and $f$ is a given function.