The area bounded by the x-axis and the parabola $y = 3x-x^2$ is:

$\frac{9}{2}$ Sq.unit

The correct answer is Option (2) → $\frac{9}{2}$ Sq.unit **

Area = $\displaystyle\int_{0}^{3}\big(3x - x^{2}\big)\,dx$

=$\left[\frac{3}{2}x^{2}-\frac{1}{3}x^{3}\right]_{0}^{3}$

=$\left(\frac{3}{2}\cdot 9 - \frac{1}{3}\cdot 27\right)-0 = \frac{27}{2}-9 = \frac{9}{2}$