Explanation

(a)
We have,
$\int_{0}^{2}{|x - 1|dx = \int_{0}^{1}{- (x - 1)dx + \int_{1}^{2}{(x - 1)dx}}}$
$= - \left\lbrack \frac{x^{2}}{2} - x \right\rbrack_{0}^{1} + \left\lbrack \frac{x^{2}}{2} - x \right\rbrack_{1}^{2}$
$= \left\lbrack - \left( \frac{1}{2} - 1 \right) - (0 - 0) \right\rbrack + \left\lbrack \left( \frac{4}{2} - 2 \right) - \left( \frac{1}{2} - 1 \right) \right\rbrack = 1$