Answer
$F^{'}(x)=\sec^{3} {x}$
Work Step by Step
$F(x)=\int_0^{x} (\sec^{3} {t}) {dt}$
$Fâ˛(x)=\frac{d}{dx}\int_0^{x} (\sec^{3} {t}) {dt}$
$=\sec^{3} {x}$
This is valid over the domain, $t\ne\frac{{k\pi}}{2}$, where $k\in\mathbb{Z}$, where the function $f(t)=\sec^{3} {t}$ is a continuous.
