Explanation

(b)
$\int_{0}^{4}{|x - 1|dx = \int_{0}^{1}{(1 - x)dx + \int_{1}^{4}{(x - 1)dx}}}$
$= \left\lbrack x - \frac{x^{2}}{2} \right\rbrack_{0}^{1} + \left\lbrack \frac{x^{2}}{2} - x \right\rbrack_{1}^{4}$
$= 1 - \frac{1}{2} + \left\lbrack 8 - 4 - \left( \frac{1}{2} - 1 \right) \right\rbrack$
$= \frac{1}{2} + 4 + \frac{1}{2} = 5$