Primitive function/Piecewisely defined/1/Exercise

Compute the definite integral ${\int }_0^{8}f(t)dt$, where the function $f$ is

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

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