Calculus: Early Transcendentals, Chapter 6, 6.1, Section 6.1, Problem 11

Refer the attached image, Graph of x=1-y^2 is plotted in blue color and graph of x=y^2-1 is plotted in red color.
The curves intersects at y=+- 1
Area of the region enclosed by the given curves A=int_(-1)^1((1-y^2)-(y^2-1))dy
A=int_(-1)^1(2-2y^2)dy
A=2*2int_0^1(1-y^2)dy
A=4[y-y^3/3]_0^1
A=4(1-1^3/3)
A=4(2/3)
A=8/3