The function |x|+|y|=1 has 4 cases.
By sketching a graph we can find that the area bounded by the curve |x|+|y|=1 is represented by the shaded region as shown in the fig:
The curve intersects the points (0,1),(1,0),(0,-1),(-1,0).
It can also be observed that the curve is symmetrical about x-axis and also y-axis.
We can conclude that the required area can be taken as 4$\times $area of OBAO.
on integrating we get,
on applying the limits we get,
Hence the required area is 2sq.units