Posted by Shelby on Sunday, October 2, 2011 at 10:55pm.
You have Int[f(x)] = F(a)
To maximize F(a), you want its derivative f(a) to be zero.
4-a^2 = 0 when a = -2 or 2
Knowing what you do about cubics, you know the max on [0,4] will occur at a = 2.
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