$(4$ points$)$ Consider the following graph for the function $f(t)$ on $0,5.$

Let $F(x)={\displaystyle \underset{0}{\overset{x^2}{}}}f(t)dt$ for xin$[0,5].$

$($a$)$ Find $F^r(1)$ and $F^r(\sqrt[\phantom{2}]{3}).$

$($b$)$ Find all critical numbers of $F(x)$ in the interval $(0,5).$

$($c$)$ Find the absolute minimum and maximum of $F(x)$ in the interval $0,5.$