If we have an entire function $f(z)$, can we apply the Cauchy integration formula for derivative for $f(z)$ and integrate over $\Bbb R$ instead of simple closed curve, i.e.
is this formula is true:
$$f'(a_{0}) = \frac{1}{2\pi i}\int_{\Bbb R}\frac{f(t)}{(t-a_{0})^{2}}dt$$
where $f(t)$ is just $f(z)$ with $z=t\in \Bbb R$.