Different behaviors with a for loop and a foreach loop with closures

I can't explain an issue I've run across. Basically I get a different answer if I use lambda syntax in a foreach loop than if I use it in a for loop. In the code below I register a delegate in a "dispatcher" class. I then later wrap the delegate on the way out in another delegate and return a list of these wrapped delegates. I then execute them. The expected output of executing the wrapped function list is 1,2. However I don't see that when I combine a lambda and a foreach loop.

This is not the code that is causing the problem, but the simplest case I could make to reproduce it. I would prefer not to discuss use cases of this, I'm more curious as to why I get behavior I'm not expecting. If I use the foreach loop below with the lambda syntax it fails. If I use the new Action() syntax and a foreach it works, if I use the lambda syntax in a for loop it works. Can anyone explain what is going on here. This has me really stumped.

    public class Holder
    public Holder(int ID, Dispatcher disp)
        this.ID = ID;
    public int ID { get; set; }
    private void Something(int test) { Console.WriteLine(ID.ToString()); }

public class Dispatcher
    List<Action<int>> m_Holder = new List<Action<int>>();

    public void Register(Action<int> func)

    public List<Action<int>> ReturnWrappedList()
        List<Action<int>> temp = new List<Action<int>>();

        //for (int i = 0; i < m_Holder.Count; i++)      //Works - gives 1, 2
        //    var action = m_Holder[i];
        //    temp.Add(p => action(p));

        foreach (var action in m_Holder)
            temp.Add(p => action(p)); //Fails - gives 2,2
            //temp.Add(new Action<int>(action)); Works - gives 1,2

        return temp;

class Program
    static void Main(string[] args)
        var disp = new Dispatcher();
        var hold1 = new Holder(1, disp);
        var hold2 = new Holder(2, disp);
        disp.ReturnWrappedList().ForEach(p => p(1));


This is the infamous "closing over the loop variable" gotcha.

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