Numerator becomes x(x^2 - 1) + x^2 - 1
Split the fraction in to two, factorise denominator as difference of two squares and simplify.
One function is odd so that becomes 0, other one becomes tan^{-1}x
As x -> infinity, tan^{-1}x \rightarrow \frac{\pi}{2}
As x-> -infinity, tan^{-1}x...