How can I find an approximate solution to this integral?

Question

I am stuck in integrating the following integral $I(x) = \int_{a}^{b}t^{2}e^{-xf(t)}\,dt$ where $f(t)=(1-e^{-t})^2$. The main problem here is at the point where $f(t)$ is zero, $t^2$ is zero. I am not sure how to evaluate this integral. Thank you very much in advance.