Why do I have to assign a value to an int in C# when defaults to 0?

This works:

class MyClass
{
    int a;

    public MyClass()
    {
        int b = a;
    }
}

But this gives a compiler error ("Use of unassigned local variable 'a'"):

class MyClass
{
    public MyClass()
    {
        int a;
        int b = a;
    }
}

As far as I can tell this happens because in the first example, technically, the compiler doesn't know that 'a' is not assigned. In the latter example, 'a' is defined locally, and therefore is easy to track.

But why does the latter example not work?

Don't integers default to 0? Is this something the compiler enforces for "best practices". Or is there another reason?