Find the area of the region bounded by the curves $\displaystyle x^{2}=y, y=x+2$ and x-axis, using integration.

Let Correct Graph : $\displaystyle x$ coordinates of point of intersection are $\displaystyle -1,2$ Required area $\displaystyle =\int_{-2}^{-1}(x+2) d x+\int_{-1}^{0} x^{2} d x$ $\displaystyle =\left.\frac{(x+2)^{2}}{2}\right|_{-2} ^{-1}+\left.\frac{x^{3}}{3}\right|_{-1} ^{0}$ $\displaystyle =\frac{1}{2}+\frac{1}{3}=\frac{5}{6}$