Bug introduced in 9.0 or earlier and persisting through 11.0.1 or later
I'm creating solution sets for a calculus course and need to shade the region in $\mathbb R^2$ such that $x^2 < y < x^4$. This is what I have so far:
Plot[{x^2,x^4}, {x, -2, 2},PlotRange->{-1,5},PlotStyle->{Automatic,Red},
Filling->{1->{{2},{LightBlue,White}}}]
Unfortunately this gives me the following picture. In particular, the region in the interval $(-1,0)$ is shaded. How can I avoid this?