Answer
$a=-\sqrt 2; b=\sqrt 2$
Work Step by Step
Following the hint given in the statement, we have
$x^4 -2x^2 \le 0$
This implies that
$x^2(x^2-2) \le 0$
Thus, we have $x=0$ or, $x^2 \leq 2$
Also, $- \sqrt 2 \leq x^2 \leq \sqrt 2$
Thus, the limits that maximize the integral are: $a=-\sqrt 2; b=\sqrt 2$