Problem $5$: Determine the value $of$ the following integrals

$(a){\displaystyle \underset{1}{\overset{7}{}}}(t+3)dt$

$(b){\displaystyle \underset{1}{\overset{7}{}}}(t-6)dt$

$(c)\{$:${\displaystyle \underset{1}{\overset{7}{}}}(2t^4-5t^3-7t^2-1)(t-8))dt$

$(d){\displaystyle \underset{1}{\overset{7}{}}}ln(t^2)(t-e)dt$