use newtons formula
u get
g'(x)=cos^4(x)
now integrate ,constant c=0 , use newtons formula
u get
g(x)=integral(cos^4(x))+c=0;
cos^4x=cos^2x * cos^2x;
replace 1 cos^2x by sin^2x;
u get g(x);
replace x by x+pi; u get the answer.
hope it is useful.rate me if it is correct!!!