Should I use int or Int32

They both declare 32 bit integers, and as other posters stated, which one you use is mostly a matter of syntactic style. However they don't always behave the same way. For instance, the C# compiler won't allow this:

public enum MyEnum : Int32
{
    member1 = 0
}

but it will allow this:

public enum MyEnum : int
{
    member1 = 0
}

Go figure.

ECMA-334:2006 C# Language Specification (p18):

Each of the predefined types is shorthand for a system-provided type. For example, the keyword int refers to the struct System.Int32. As a matter of style, use of the keyword is favoured over use of the complete system type name.

The two are indeed synonymous; int will be a little more familiar looking, Int32 makes the 32-bitness more explicit to those reading your code. I would be inclined to use int where I just need 'an integer', Int32 where the size is important (cryptographic code, structures) so future maintainers will know it's safe to enlarge an int if appropriate, but should take care changing Int32s in the same way.

The resulting code will be identical: the difference is purely one of readability or code appearance.