The area of the region bounded by the curves $y=x^2,y=|2-x^2|$ and $y=2$ which lies to the right of the line $x = 1$, is

$\left(\frac{20-12\sqrt{2}}{3}\right)$ sq. units

Let A be the required area. Then,

A = Area ABCA + Area BCD

$⇒A=\int\limits_1^{\sqrt{2}}\{x^2-(2-x^2)\}dx+\int\limits_{\sqrt{2}}^2\{2-(x^2-2)\}dx$

$⇒A=\int\limits_1^{\sqrt{2}}(2x^2-2)dx+\int\limits_{\sqrt{2}}^2(4-x^2)dx$

$⇒A=\left[\frac{2}{3}x^3-2x\right]_1^{\sqrt{2}}+\left[4x-\frac{x^3}{3}\right]_{\sqrt{2}}^2=\left(\frac{20-12\sqrt{2}}{3}\right)$ sq. units