Dual booting means that you get a choice at startup to run either operating system; it sounds like that's what you have going on. It's easy to get the official AMD drivers for the Radeon HD4200 from this point:
■Boot into Ubuntu.
■From the Ubuntu desktop, click on System>Administration>Additional Drivers.
■Once it finishes searching, Ubuntu will present you with a list of proprietary drivers. Click on the ATI driver and then click "Activate".
■Reboot the computer and go back into Ubuntu.
■At this point, you should be running the official AMD drivers!