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[Manolo Sobrino]

No Tim, that is (or should be) completely intentional, unless you understand that the X in the integrand is a dummy variable, but this is in fact an abuse of notation as a definite integral in which you integrate over a variable which is also a limit makes no sense(*).

You are dealing with functions defined by integrals. The function depends just on the limit(s) of the integral and the proper way to write that is by using different variables for the integrand.

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(*) BTW Mathematica does this... and it's dumb, because imagine that you define the function:

F[y_]:=Integrate[x, {x, 0, y}]

Now you evaluate, for instance at y=2, and you get:

F[2]=2

Which is fine.

As we are happy with Mathematica understanding:

Integrate[x, {x, 0, x}] = x^2/2

Let's do the same

F[x_]:=Integrate[x, {x, 0, x}]

So far, so good, but let's use this at x=2

F[2]

... and of course we get:

Integrate::ilim: "Invalid integration variable or limit(s) in {2,0,2}."

As you are trying to do this:

Integrate[2, {2, 0, 2}]

Maybe abusing notation is convenient for a while, but in a CAS it will end badly.