Explanation

(c)
Let $I = \int_{2}^{4}{\left\{ |x - 2| + |x - 3| \right\} dx}$
$= \int_{2}^{3}{\left\{ (x - 2) + (3 - x) \right\} dx + \int_{3}^{4}{\left\{ (x - 2) + (x - 3) \right\} dx}}$
$= \int_{2}^{3}{dx + \int_{3}^{4}{(2x - 5)dx}}$
$= \lbrack x\rbrack_{2}^{3} + \left\lbrack x^{2} - 5x \right\rbrack_{3}^{4}$
$= 3 - 2 + \lbrack 16 - 20 - (9 - 15)\rbrack$
$= 1 + 2 = 3$