Đặt $x=2sint\Rightarrow dx=2costdt$Đổi cận: $x=-1\Rightarrow t=-\frac{\pi}{6},x=\sqrt{2}\Rightarrow t=\frac{\pi}{4}$
$I=\int\limits_{-\pi/6}^{\pi/4}4sin^2t.\sqrt{4-4sin^2t}.2costdt$
$=\int\limits_{-\pi/6}^{\pi/4}16sin^2tcos^2tdt$
$=\int\limits_{-\pi/6}^{\pi/4}4sin^22tdt$
$=\int\limits_{-\pi/6}^{\pi/4}2(1-cos4t)dt=2t-\frac{1}{2}sin4t|\tfrac{pi/6}{-\pi/4}=\frac{5\pi}{6}-\frac{\sqrt{3}}{4}$