Defining a constant in Mathematica

[ToxicBug]

Hello, I've been breaking my head over this for a couple hours now.

I'm trying to find the expected value of a Gumbel distribution.

Integrate[ y*E^(-((y - a)/b))*E^(-E^(-((y - a)/b)))/b, {y, -Infinity, Infinity},
  Assumptions -> b > 0]

If I set a = 2 and b = 5, it works. Otherwise it gives me a very complicated expression. I've tried SetAttributes[a, Constant], but it doesn't do the trick. Anyone know how can I solve this?

 

[CompuChip]

Try giving it some information about a, like

Assumptions -> b > 0 && Element[a, Reals]