Out of these three, is only the last one proper?
Impossible to tell. There are no limits specified.
This might help:
Improper integral - Wikipedia, the free encyclopedia
I will summarise the other responses that you have had:
We do not really know what you mean by proper/improper in the context of these integrals (one of the responses may contain the answer that you need but I cannot tell).
Tell us what definition for the term proper you are working with.