How to select a normalization method?

[morenopo2012]

What are the applications to normalize to 1?
what is the difference between the integral of de function in all the space equal to 1 with normalize to 1?

 

[Stephen Tashi]

Are are asking for someone to list all the different situations in science and mathematics where it is useful to normalize a function to 1? You'll have better luck if you ask about a single particular situation.