int (0 pi/2) cos^2 t dt = int (0 pi/2) (1 + cos 2t)/2 dt =
= 1/2 * int (0 pi/2) (1 + cos 2t) dt = 1/2 * (t + 1/2 * sin 2t)_{0}^{pi/2} =
= 1/2 * ((pi/2 + 1/2 * sin pi) - (0 + 1/2 * sin 0)) = 1/2 * pi/2 = pi/4.