- the blue shaded region above

To define the bounds, we need to find the points of intersection. We know that at the points of intersection, both the equations are satisfied.

⇒ x + y = 0

⇒ x + (2 – x²) = 0 (from the other equation)

So, x² – x – 2 = 0 i.e., (x - 2)(x + 1) = 0 or x = -1,2

So, bounds are x = -1 to x = 2

Therefore, area shall be evaluated as –

(Ans)