lifetime of local variable inside an Action in c# [duplicate]

Lifetime of local variable declared inside a method is limited to the execution of that method. But in the following code sample lifetime of local variable index preserved after the execution of method .

class Program { static Action action; static void Main(string[] args) { setAction(); for (int i = 0; i < 5; i++) { action(); } Console.ReadLine(); } static void setAction() { var index = 5; action = () => { index++; Console.WriteLine("Value in index is {0}",index); }; } } 

The output of the program is this

Value in index is 6 Value in index is 7 Value in index is 8 Value in index is 9 Value in index is 10 

I can not understand how the values in variable index is preserved.