\(\int^{\frac{\pi}{2}} _{\frac{-\pi}{2}} cos x dx = [sinx]^{\frac{\pi}{2}} _{\frac{-\pi}{2}}\) =sin\(\frac{\pi}{2} - sin\frac{-\pi}{2}\) = sin90 – sin(-90) = sin90 – sin270 = 1 – (-1) = 1+1 = 2