Integral estimation

[teralion98]

Hi! How can I get these inequalities? I have tried to use mean value theorems, estimate the integrand, but nothing had gave me acceptable accuracy
[math]\frac{e^2-1}{e^{e^2}-1}<\int_{1/e}^{e}x^2 e^{-x^2} dx < \frac{e^2-1}{e^2}[/math]

 

[blamocur]

Can you find the minimum and the maximum values of the integrand?