If the area of the region {(x, y): 1-2 x ≤ y ≤ 4-x^2, x ≥ 0, y ≥ 0} is (α)/(β), α, β ∈ N, gcd (α, β)=1, then the value of (α+β) is:

If the area of the region $\displaystyle \left\{(x, y): 1-2 x \leqslant y \leqslant 4-x^2, x \geqslant 0, y \geqslant 0\right\}$ is $\displaystyle \frac{\alpha}{\beta}, \alpha, \beta \in \mathbf{N}, \operatorname{gcd}(\alpha, \beta)=1$, then the value of $\displaystyle (\alpha+\beta)$ is :