Hint:
y = 4 - x\(^2\) and y = 2x + 1
=> 4 - x2 = 2x + 1
=> x2 + 2x - 3 = 0
(x+3)(x-1) = 0
thus x = 1 or x = -3.

Integrating x\(^2\) + 2x - 3  

= 3x - x\(^2\) - \(\frac{x^3}{3}\) 

from (1, to -3) : 3 (1) - 1\(^2\) - \(\frac{1^3}{3}\) - 3 (-3)  -  -3\(^2\) - \(\frac{-3^3}{3}\) 

= \(\frac{5}{3}\) + 9 

 will give 32/3 = 10 \(\frac{2}{3}\)