Explanation

(b)
$\int_{1}^{4}{|x - 3|dx = \int_{1}^{3}{(3 - x)dx + \int_{3}^{4}{(x - 3)dx}}}$
$= \left\lbrack 3x - \frac{x^{2}}{2} \right\rbrack_{1}^{3} + \left\lbrack \frac{x^{2}}{2} - 3x \right\rbrack_{3}^{4}$
$= \left( 9 - \frac{9}{2} \right) - \left( 3 - \frac{1}{2} \right) + \left( \frac{16}{2} - 12 \right) - \left( \frac{9}{2} - 9 \right)$
$= \frac{5}{2}$