new vs override keywords

I've got a question concerning polymorphic methods. I've got two classes: the base class with the non-virtual method Foo( ) which calls its virtual method Foo (int i) (like this: Foo() {Foo(1);}) and the derived class which overrides method Foo(int i).

If I call Foo() method of an instance of the derived class the walkthrough is as the following: base Foo() -> override Foo(int i). But if I change override method to new the walkthrough is as the following: base Foo -> base Foo(int i). It doesn't even get to the new Foo(int i) method. Please, explain the sequence of those methods and why it is the way it is.

using System;
class Program
{
    sealed void Main()
    {
        DerivedClass d = new DerivedClass();
        //Goes to BaseClass Foo() method
        //then goes to Derived Foo(int i ) method
        d.Foo();
    }
}
class BaseClass
{
    public void Foo() { Foo(1); }
    public virtual void Foo(int i) { // do something;
    }
}
class DerivedClass : BaseClass
{
    public override void Foo(int i)  { //Do something
    }
}

//////////////////////////////////////////////////////////////////////

using System;
    class Program
    {
        sealed void Main()
        {
            DerivedClass d = new DerivedClass();
            //Goes to BaseClass Foo() method
            //then goes to base Foo(int i) method
            //never gets to Foo(int i)  of the derived class
            d.Foo();
        }
    }
    class BaseClass
    {
        public void Foo() { Foo(1); }
        public virtual void Foo(int i) { // do something;
        }
    }
    class DerivedClass : BaseClass
    {
        public new void Foo(int i)  { //Do something
        }
    }