Restoring some data after iPhone restoration

Just did a restore to factory settings because Apple said I was having some software related battery issues.

I lost a lot of app data, and I'd like to restore it if possible. I think I still have backups from a couple days ago. Would this stuff be stored in the iTunes backups?:
- pictures/camera roll
- calendar
- reminders
- alarms
- messages
- safari bookmarks

There might be a couple similar things I'm forgetting. The odd thing is it appears a few things of this nature already did get restored, such as my notes, but I can't seem to find the stuff above.

Thanks