Question: Combining function notation with integration template

I'm trying to have Maple work through ideas involving the Fundamental Theorem of Calculus, and am encountering a problem with the programming of Maple.

I begin by defining a function like:

F(x) := int(x^2,x)  (or equivalently, F:= x -> int(x^2,x)  )

Then I ask Maple to evaluate F(2).  I expect to get 8/3 but instead I get this error message:

Error, (in int) integration range or variable must be specified in the second argument, got 2

Any thoughts or suggestions on how to have Maple work through this idea as closely as possible to the textbook style development of F(x) = int(f(x),x), then computing F(b)-F(a) as I really want?

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