Explanation

(b)
$\int_{0}^{10}{\left| x(x - 1)(x - 2) \right|dx}$
$= \int_{0}^{1}{\left( x^{3} - 3x^{2} + 2x \right)dx + \int_{1}^{2}{\left( - x^{3} + 3x^{2} - 2x \right)dx}}$
$= \int_{2}^{10}{\left( x^{3} - 3x^{2} + 2x \right)dx}$
$= \left\lbrack \frac{x^{4}}{4} - x^{3} + x^{2} \right\rbrack_{0}^{1} + \left\lbrack - \frac{x^{4}}{4} + x^{3} - x^{2} \right\rbrack_{1}^{2} + \left\lbrack \frac{x^{4}}{4} - x^{3} + x^{2} \right\rbrack_{2}^{10}$
$= 1600.5$