Compute the derivatives of the following functions:

$($a$)F(x)={\displaystyle \underset{0}{\overset{x}{}}}\frac{1}{t^3+1}dt$

$($c$)F(x)={\displaystyle \underset{x^2}{\overset{0}{}}}sin(cost)dt$

$($b$)F(x)={\displaystyle \underset{0}{\overset{x^2}{}}}\frac{1}{t^3+1}dt$

$($d$))$dt

Please show work