How can I restore from a iPhone backup from the /appdata/backup folder? The backup I want is not listed in iTunes.

I backed up my iPhone just after updating to 5.1.1 via iTunes. Then I erased all the data and settings as I was encountering an error with an application. I want to restore my iPhone with that backup. However, iTunes doesn't list the prior backup in the backup from field. The /appdata/backup folder does contain my backup though. How can I choose to use that backup, or use the data from that backup? I have read about the iPhone Backup Extractor application for OS X, but I am not too sure how to use it. Thanks.