Let $A_1$ be the bounded area enclosed by the curves $y=x^2+2$, $x+y=8$ and the y-axis that lies in the first quadrant. Let $A_2$ be the bounded area enclosed by the curves $y=x^2+2$, $y^2=x$, $x=2$, and the y-axis that lies in the first quadrant. Then $A_1-A_2$ is equal to

• A
  $\frac{2}{3}(2\sqrt{2}+1)$
• B
  $\frac{2}{3}(4\sqrt{2}+1)$
• C
  $\frac{2}{3}(\sqrt{2}+1)$
• D
  $\frac{2}{3}(3\sqrt{2}+1)$