Explanation

(c)
Let $\int_{0}^{1.5}{\lbrack x^{2}\rbrack dx} = \int_{0}^{1}{\left\lbrack x^{2} \right\rbrack dx + \int_{1}^{\sqrt{2}}{\left\lbrack x^{2} \right\rbrack dx + \int_{\sqrt{2}}^{1.5}{\left\lbrack x^{2} \right\rbrack dx}}}$
$= \int_{0}^{1}{0dx + \int_{1}^{\sqrt{2}}{1\ dx + \int_{\sqrt{2}}^{1.5}{2\ dx = 2 - \sqrt{2}}}}$