[JadeNB]

> Hey look, you don't need the dummy variable explicitly any more. It's almost like it's a relic from a time before people understood what function application actually was.

If you actually perform definite integration, as a limit of Riemann (or Lebesgue, if you like) sums, or even try to approximate it numerically, you're going to have some dummy variable cropping back up again. As your comment indicates, when Risch's theorem proves that there is no elementary anti-derivative, you're going to be out of luck.