The area (in sq. units) bounded by \(x^2=y, y=x+2\) and the \(\mathrm{X}\)-axis is

Indicate the region bounded by the curves \(x^2=y, y=x+2\) and \(X\)-axis and obtain the area enclosed by them. The parabola and line meet in points \(P(-1,1)\) and \(Q(2,4)\). The line cuts the axes in \((-2,0)\) and \(B(0,2)\). Here, we have to find the area bounded by the curves and \(X\)-axis i.e. area \(O R A P Q\) i.e. area \(A P R+\) area \(P R O\)
\(\begin{aligned} & =\int_{-2}^{-1} y_{\text {line }} d x+\int_{-1}^0 y_{\text {parabola }} d x \\ & =\int_{-2}^{-1}(x+2) d x+\int_{-1}^0 x^2 d x \\ & =\left[\frac{x^2}{2}+2 x\right]_{-2}^{-1}+\left[\frac{1}{3} x^3\right]_{-1}^0 \\ & =\frac{1}{2}+\frac{1}{3}=\frac{5}{6} \text { sq units } \end{aligned}\)