When I shut down I uncheck the box to not reopen programs at start up but they r still open when I start up my MacBook 2011 13 inch
What kind of programs are they? You can try to uncheck startup programs here: System Preferences/Users & Groups/Login Items
Maybe 'cause they were open when you shut your Mac off. I think the feature is called "Resume", they added it with Lion. When you shut down, there should be an option to choose whether or not to open the apps you already have open on the next startup.