cin.eof() functionality

I understand that cin.eof() tests the stream format. And while giving input, end of character is not reached when there is wrong in the input. I tested this on my MSV C++ 2010 and am not understanding the strange results. No matter what I give the input, I am getting Format Error message that is present in the program.

#include <iostream>
using namespace std;

int main()
{
    int i;
    cin>> i;

    if(!cin.eof())
    {
        cout<< "\n Format Error \n";
    }
    else
    {
        cout<< "\n Correct Input \n";
    }

    getchar();
    return 0;
}

Results I expected:

Values for i =

1. 10 => Correct Input but the output is Format Error
2. 12a => Format Error

Could someone explain where I am going wrong. Thanks.