The area of the region $\left\{(x, y): x^{2} \leq y \leq\left|x^{2}-4\right|, y \geq 1\right\}$ is

Question

$\frac{4}{3}(4 \sqrt{2}+1)$

$\frac{3}{4}(4 \sqrt{2}+1)$

$\frac{4}{3}(4 \sqrt{2}-1)$

$\frac{3}{4}(4 \sqrt{2}-1)$

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