The area bounded by the curves $y=|x|-1$ and $y=-|x|+1$ is:

The region is bounded by four lines:For $x>0$: $y=x-1$ and $y=-x+1$ For $x<0$: $y=-x-1$ and $y=x+1$ Plotting these points:Intersections with axes: $(1,0),(-1,0),(0,1),(0,-1)$.These four points form a square (or a rhombus).The diagonals of this figure lie on the $x$ -axis and $y$ -axis.Length of diagonal on $x$ -axis $=1-(-1)=2$.Length of diagonal on $y$ -axis $=1-(-1)=2$.Area of a rhombus $=\frac{1}{2}\times d_1\times d_2$ $
$\text{Area}=\frac{1}{2}\times 2\times 2=2\text{ sq units}$ $