definite integration

0 = cos x + 1/2 => cos x = -1/2 => x = 2π/3The curve is above the x-axis from x = 0 to x = 2π/3The curve is below the x-axis from x = 2π/3 to x= πArea of the 2 parts = ∫ (cos x + 1/2)dx [0 to 2π/3] + ∫-(cos x +1/2)dx [2π/3 to π]= [sin x +x/2] 0 to 2π/3 + [-sin x – x/2] 2π/3 to π= √3/2 + π/3 – π/2 + √3/2 + π/3 = √3 + π/6