Two weeks notice question?

So I have found a new job that wants me to start on July 11th. I gave two weeks to my employer on Friday, but since I am out of the office for three days this week they wanted me to stay a few extra days so that I'm in for ten days. I'm not sure I want to and know I have no obligation to. I want to be professionally courteous though since they have employed me for three years? What would you do if you were in my shoes? Thanks!