Verified answer

By the Fundamental Theorem of Calculus we know that F'(x) = (1 - x^2)*cos^2(x).

Now since cos^2(x) > 0 for all x except x = (pi/2) + n*pi for any integer n,

and (1 - x^2) > 0 for lxl < 1, we can conclude that, since cos^2(x) > 0 on lxl < 1,

the function F(x) is increasing on the interval (-1 , 1).