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Filling area between curves


I have 3 curves, and I want to fill one of the areas that they bound.
The equations are
F[x] = -1 + 4 x - x^2
G[x] := x - 2
H[x] := 2 - x
and I want to fill the region that I shaded in this picture:
http://i.imgur.com/X2urH.png

I've been trying to figure this out on my own, but to no avail. How do
I do this?



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