Hey tastylick.
Hint: Your x limits should be from -pi to +pi (as you have suggested). Using this gives us
Integral [0,pi/2] sin(y)[-cos(pi) + cos(-pi)]dy
Integral [0,pi/2] sin(y)[-1-1]
Integral [0,pi/2[ -2*sin(y)
= 2[cos(pi/2) - cos(0)] = -2.
Hey tastylick.
Hint: Your x limits should be from -pi to +pi (as you have suggested). Using this gives us
Integral [0,pi/2] sin(y)[-cos(pi) + cos(-pi)]dy
Integral [0,pi/2] sin(y)[-1-1]
Integral [0,pi/2[ -2*sin(y)
= 2[cos(pi/2) - cos(0)] = -2.