iPhone 4 restore to a replacement phone

I recently got a replacement iPhone 4 (under warranty to replace my old iPhone 4), and just before returning the old iPhone 4, I did a backup. When I connect the new phone to my iTunes, it only gives me the option to register the phone and does not offer me an option to restore. My new phone's iOS is 5.0.1; I can't recall if my old phone was on 5.1 or 5.0.1. I'm worried to update the iOS of the new phone to 5.1, in case my old backup wasn't on 5.1. Can a backup done on an older version restore to a new phone on a newer version?

Solution 1:

You have to register/activate the phone first before you can restore it from backup. Even in case you won't get asked during/after activation, you can always connect your phone to iTunes later and click on Restore.