For a continuos random variable $X$, if we have its p.d.f. $f(x)$, then the cumulative densitity function (c.d.f.) of $X$, $F(x)$, is
$F(x) = \int_{-\infty}^{x}f(t)dt$ We also have $F'(x) = \frac{d}{dx}F(x)= f(x)$
Why does the last step in the following equation yields $f(x)$?
$\frac{d}{dx}F(x) = \frac{d}{dx} \int_{-\infty}^{x}f(t)dt = \int_{-\infty}^{x} \frac{\partial}{\partial x} f(t)dt $