SQL Server 2005 VS 2005 Web App - Connection Pooling

In a Web app as per above, where are connections to SQL Server and the connection pool monitored?  Is it in SQL Server itself?

For example, in the following connection string:
"Server=(local); Database=TranOps; " +
                "Integrated Security=SSPI;" +
                "Pooling = true;" +
                "Min Pool Size = 1;" +
                "Max Pool Size = 5;" +
                "Persist Security Info=False;";
The first user accesses a web form, and the connection is opened, and the pool started, then the connection is closed.  I think at this point there should be five connections available.
When the second user accesses their web form, and connects using exactly the same string,  it seems that if the connection is requested within a certain time frame of the first, one of the original five connections will be 'opened', or more correctly drawn from the pool, and used.
If I am understanding this correctly, then the pool must be maintained by SQL Server, not by anything in the web application. Is this a correct interpretation?
 
Many thanks,
Mike Thomas