∫(0->π) sin²x dx
= (1/2)∫(0->π) (1-cos2x) dx
= (1/2)(x - 1/2*sin2x),(0->π)
= (1/2)(π - 1/2*sin2π) - (1/2)(0 - 1/2*sin0)
= (1/2)(π - 0) - 0
= π/2