Chapter 5.5, Problem 18ES

In each part, evaluate the integral, given that

$f\left(x\right)=\left\{\begin{array}{cc}2x,& x\le 1\\ 2,& x>1\end{array}\right.$

(a) ${\displaystyle {\int }_0^{1}f\left(x\right)dx}$

(b) ${\displaystyle {\int }_{-1}^{1}f\left(x\right)dx}$

(c) ${\displaystyle {\int }_1^{10}f\left(x\right)dx}$

(d) ${\displaystyle {\int }_{1/2}^{5}f\left(x\right)dx}$