Primitive function/Piecewisely defined/1/Exercise

Compute the definite integral ${}\int _{0}^{8}f(t)dt$, where the function ${}f$ is

${}f(t)={\begin{cases}t+1,{\text{ if }}0\leq t\leq 2\,,\\t^{2}-6t+11,{\text{ if }}2<t\leq 5\,,\\6,{\text{ if }}5<t\leq 6\,,\\-2t+18\,,{\text{ if }}6<t\leq 8\,.\end{cases}}\,$

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