Integrating $\int^2_{-2}\frac{x^2}{1+5^x}$ $$\int^2_{-2}\frac{x^2}{1+5^x}$$
How do I start to integrate this?
I know the basics and tried substituting $5^x$ by $u$ where by changing the base of logarithm I get $\frac{\ln(u)}{\ln 5}=x$, but I got stuck.
Any hints would suffice preferably in the original question and not after my substitution.
(And also using the basic definite integrals property.)
Now I know only basic integration, that is restricted to high school, so would prefer answer in terms of that level.

Hint:
$$\frac1{1+5^{-x}} + \frac1{1+5^x} = 1$$
