The area (in sq. units) of the region A = {(x,y): x² ≤ y ≤ x+2} is?

Correct option is B.
9/2
x² ≤ y ≤ x+2
x² = y; y = x+2
x² = x+2
x² - x - 2 = 0
(x-2)(x+1) = 0
x = 2, -1
Area = ∫₋₁² (x+2) - x² dx = [x²/2 + 2x - x³/3]₋₁² = 2 + 4 - 8/3 - (1/2 - 2 + 1/3) = 2 + 4 - 8/3 - 1/2 + 2 - 1/3 = 9/2.