Explanation

(d)
$\int_{1}^{3}{(x - 1)(x - 2)(x - 3)dx}$
$= \int_{1}^{3}{(x - 1)\left( x^{2} - 5x + 6 \right)dx}$
$= \int_{1}^{3}{\left( x^{3} - 6x^{2} + 11x - 6 \right)dx}$
$= \left\lbrack \frac{x^{4}}{4} - \frac{6x^{3}}{3} + \frac{11x^{2}}{2} - 6x \right\rbrack_{1}^{3}$
$= \left\lbrack \frac{81}{4} - \frac{162}{3} + \frac{99}{2} - 18 - \left( \frac{1}{4} - \frac{6}{3} + \frac{11}{2} - 6 \right) \right\rbrack$
$= \left\lbrack - \frac{27}{12} + \frac{27}{12} \right\rbrack = 0$