A Bit Tricky

$f(a,b) = \int_{b}^{a}\dfrac{x^2 \, dx}{\sqrt{1-x^2}}$ $g(a,b) = \int_{a}^{b}\dfrac{x^2 \, dx}{\sqrt{1-x^2}-1}$ If $a^2-b^2 = 1$ , find the value of $\left \lfloor \max((f+g)(a,b)) \right \rfloor- \left \lfloor \min((f+g)(a,b)) \right \rfloor \; .$