Problem - 3642
Find all functions $f:\mathbb{R}\rightarrow\mathbb{R}$ such that $$x^2f(x)+f(1-x)=2x-x^4$$
Replacing $x$ with $1-x$, we have $$(1-x)^2f(1-x)+f(x)=2(1-x)-(1-x)^4$$
Treating $f(x)$ and $f(1-x)$ and solving these two equations give $f(x)=\boxed{1-x^2}$.