The area bounded by the curve y = x³, the x-axis and the ordinates x = –2 and x = 1 is

17/4

The bounded area is shown shaded in the fig.

The required Area = Area(OABO) + Area(OCDO)

$=\begin{vmatrix}\int\limits_0^1x^3dx\end{vmatrix}+\begin{vmatrix}\int\limits_{-2}^0x^3dx\end{vmatrix}=\begin{vmatrix}\frac{x^4}{4}\end{vmatrix}_0^1+\begin{vmatrix}\frac{x^4}{4}\end{vmatrix}_{-2}^0$

$=\frac{1}{4}+4=\frac{17}{4}$ sq. units.

Hence (D) is the correct answer.