The area of the region bounded by the curves $y = x^2+2,y=x,x=0$ and $x = 2$ is

$\frac{14}{3}$ Sq. units

The correct answer is Option (3) → $\frac{14}{3}$ Sq. units

Required area $=\displaystyle \int_{0}^{2}\big[(x^{2}+2)-x\big]\,dx=\int_{0}^{2}(x^{2}-x+2)\,dx$

$=\left[\frac{x^{3}}{3}-\frac{x^{2}}{2}+2x\right]_{0}^{2}=\frac{8}{3}-2+4=\frac{14}{3}$

Area $=\frac{14}{3}$