Problem with an integral

Prove that $lim_{cto 1^{-}} int_{-c}^{c} frac{xdx}{(x^{2}-1)^{2}} = 0$

Does this imply that $int_{-1}^{1} frac{xdx}{(x^{2}-1) ^{2}}$ converges to 0 ? Graph the integrand over (-1, 1) and explain what is going on.