I_2=\int_{|x|\leq 1} \frac{n}{\sqrt{\pi}}e^{-n^2 x^2}h(x)dx\leq \frac{2Cn}{\sqrt{\pi}}\int_0^1 xe^{-n^2 x^2}dx=\frac{C}{n\sqrt{\pi}}(1-e^{-n^2})