Explanation

(d)
$\int_{0}^{2}{(3x)dx = \int_{0}^{2}{\left( 3x - \lbrack 3x\rbrack \right)dx}}$
$= 3 \bullet \int_{0}^{2}xdx - \int_{0}^{2}{\lbrack 3x\rbrack dx}$
$= 3\left\lbrack \frac{x^{2}}{2} \right\rbrack_{0}^{2} - \frac{1}{3}\int_{0}^{6}{\lbrack x\rbrack dx}$ (by property)
$= 6 - \frac{1}{3}\sum_{r = 0}^{5}{\int_{r}^{r + 1}{\lbrack x\rbrack dx}}$
$= 6 - \frac{1}{3}\sum_{r = 0}^{5}r$
$= 6 - \frac{1}{3}(0 + 1 + 2 + .\ldots. + 5)$
$= 6 - \frac{1}{3} \bullet 15 = 1$