Compute the following integrals.

$($a$)$

Z $2$

$1$

xe$3$x$2$

dx

$($b$)$

Z

$0$

y sin$($y$)$ dy

$($c$)$

Z b

$/2$

$($z $+$ cos$($z$)$ sin$($z$))$ dz$,$ where b $>$ $/2$ is a constant