This is the graph of |x| + |y| = 1.

So, area within the curve = area of square ABCD = 2 sq. units.

or, by integration,

area within the curve = 4 times area of triangle AOB = 4 int x from 0 to 1 (1 - x).dx = 4(x - (x²/2)) with limit of x from 0 to 1

= 4(1 - (1/2)) = 4(1/2) = 2 sq. units.

How to draw the graph

|x| + |y| = 1

For x,y>0; eq. is x + y = 1

For x>0 and y<0; eq. is x - y =1

For x<0 and y>0; eq. is - x + y =1

For x,y<0; eq. is - x - y = 1