Question

if f'(x)=cos^2x and f(1)=0 then f(x)=

Answer 1

cos^2x = (1+cos2x)/2

f(x) = x/2 + sin2x/4 + C
at x=1,
0 = 1/2 + 0 + C
C = -1/2

f(x) = x/2 + sin2x/4 - 1/2
= 1/4 (2x + sin2x - 2)

Answer 2

0 = 1/2 + sin(2)/4 + C
C = -1/4 (2 + sin2)

adjust final answer accordingly