5.3 The Fundamental Theorem of Calculus/10

${\begin{aligned}g(r)=\int _{0}^{r}{\sqrt {x^{2}+4}}dx\\[2ex]{\frac {d}{dx}}\int _{0}^{r}{\sqrt {x^{2}+4}}dx\\[2ex]{\frac {d}{dx}}\int _{a(x)}^{b(x)}F(t)dt={\frac {d}{dx}}[b(x)]\cdot F(b(x))-{\frac {d}{dx}}[a(x)]\cdot F(a(x))\\[2ex]1\cdot {\sqrt {r^{2}+4}}-0\cdot {\sqrt {0^{2}+4}}\\[2ex]={\sqrt {r^{2}+4}}\end{aligned}}$