Find all the functions $f : [-\frac{\pi}{2}; \frac{\pi}{2}] \to \mathbb{R}$ such that:
a. $f$ is differentiable on $[-\frac{\pi}{2}, \frac{\pi}{2}]$;
b. there exists an antiderivative $F$ of $f$ such that $F(x) + f'(x) \le 0, \forall x \in [-\frac{\pi}{2}, \frac{\pi}{2}]$ and $F(-\frac{\pi}{2}) = F(\frac{\pi}{2}) = 0$.