IOS 6 ITunes Update Failed.

I have updated my IPhone 4 with IOS 6 and now am trying to update my ITunes. I go through the process of the ITunes update and I eventually get to the point where I must install and restart ITunes to complete the update, but it tells me that the app "Software update" failed to close. When I try to Force Quit this app it is not on the list of open applications.

Just wondering if anyone knows how to fix this or if I am just missing a huge step.

Thanks