$1\mathrm{.}13$ Evaluate the following integrals:

$($a$){\displaystyle \underset{1}{\overset{1}{}}}u()d$

$($b$){\displaystyle \underset{0}{\overset{4}{}}}r(t-1)dt$

$($c$){\displaystyle \underset{0}{\overset{4}{}}}(t-6{)}^2(t-2)dt$

$($d$){\displaystyle \underset{-4}{\overset{4}{}}}2t^3(t-4)dt$

Answer and show all the steps please