The area bounded by the curve $y=x^2|x|$, x-axis and the ordinates x = -1 and x = 0 is given by:

$\frac{1}{4}$ square units

The correct answer is Option (4) → $\frac{1}{4}$ square units

$y=x^2|x|=\left\{\begin{matrix}x^3&x≥0\\-x^3&x<0\end{matrix}\right.$

so area = $\int\limits_{-1}^0-x^3dx$

$=\left[-\frac{x^4}{4}\right]_{-1}^0$

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