$2.$ Let F$($x$)$ be defined asF$($x$)=$ integral from $\{$x$\}$ to $\{$arcsin x$\}$ of: cos$^2($t$)$ dt$($a$)(5$ pts$)$ Compute the derivative F$\text{'}($x$).($b$)(3$ pts$)$ Simplify your answer in part $($a$)$ completely. That is$,$ do not leave an inverse trig inside a trig function.