Random in-inclusive max

[wheretheidivides]

The 'random int' has a 'inclusive max'.  the following page does not go over what it does.
https://hutonggames.fogbugz.com/default.asp?W87

So if I say,
min=1 and max=3,
then not checked is 1 or 2?
and checked is 1, 2 or 3?

[mdotstrange]

I believe that it just uses the "max" number- so if the min is 1 and the max is 3- by checking inclusive max it will generate a 1, 2 or 3- if its unchecked it will only generate a 1 or 2