What is the area bounded by the curves |y|=1-x^2 ?

Since |y|=\left\{$\begin{array}{cc}y & y > 0 \\ -y & y < 0 \\ 0 & y=0\end{array}$\right.$ For $y > 0 \Rightarrow y=1-x^2$ For $y < 0 \Rightarrow y=x^2-1$ For $y=0 \Rightarrow x= \pm 1$ So area under the curve $=4 \times$ Area under the region OABO (symmetry)\begin{aligned}= & 4 \times \int_0^1 1-x^2 \mathrm{dx} \\ & \left.=4 \times\left[x-\frac{x^3}{3}\right]_0^1\right]\end{aligned}$$=4 \left(1-\frac{1}{3}\right)$=4 \times $\frac{2}{3}=\frac{8}{3} sq. units