Calculus: Early Transcendentals, Chapter 6, 6.1, Section 6.1, Problem 19

y=cos(pix) , y=4x^2-1
Refer the attached image. Graph of cos(pix) is plotted in blue color and graph of y=4x^2-1 is plotted in red color.
From the graph , the curves intersect at x=+- 1/2.
Area enclosed by the curves A=int_(-1/2)^(1/2)(cos(pix)-(4x^2-1))dx
A=2int_0^(1/2)(cos(pix)-4x^2+1)dx
A=2[sin(pix)/pi-4(x^3/3)+x]_0^(1/2)
A=2[sin(pix)/pi-(4x^3)/3+x]_0^(1/2)
A=2((sin(pi/2)/pi-4/3(1/2)^3+1/2)-(sin(0)/pi-4/3(0)^3+0))
A=2((1/pi-4/3(1/8)+1/2)-0)
A=2(1/pi-1/6+1/2)
A=2(1/pi+2/6)
A=2/pi+2/3