The area of the region bounded by the curves $\mathrm{y}={\mathrm{x}}^2$ and $\mathrm{y}=\frac{2}{1+{\mathrm{x}}^2}$ is ___ sq.units

$\text{ For intersection point, }{x}^2=\frac{2}{1+x^2}$

$\text{ i.e. }{x}^4+x^2-2=0$

$\text{ i.e. }\left(x^2+2\right)\left(x^2-1\right)=0$

$x=\pm 1$

$\text{ Hence, required area }=2{\int }_0^1 \left(\frac{2}{1+x^2}-x^2\right)dx$

$=2{\left[2{\tan }^{-1}x-\frac{x^3}{3}\right]}_0^1=2\left(\frac{\pi }{2}-\frac{1}{3}\right)$