Will my apps from my ios5.1 back up work on my new ios6?

I want to update my iphone to ios6 but it can't be jailbroken yet, so i backedup my apps and everything on my itunes from my ios5.1, i was wondering if i restore them after i update to ios 6 will they still work? Specially whatsapp?

Yes!
If you want to be Really sure, go to the App Store and search your app to see if its compatible with iOS6. 95.9% it's a yes. Have fun and don't use apple maps.

Whether the app is compatible or not it will be backed up and all the settings will be backed up for your apps. I would also recommend that you do the iCloud back up as well if you can. Do keep in mind that when restoring from a back up on a computer that only the photos, songs, videos, etc are backed up and not the apps unless you tell iTunes to transfer your purchases to your device, which is unnecessary and time consuming, but iTunes will restore all of this content automatically when you restore after the the update. It will restore the app settings so all you have to do is download that app again and all the settings for that app or game will be there. With the iCloud back up, it will redownload everything including apps and whatnot. This method can be very time consuming if you have a slow internet connection. Mine, if I remember correctly, took about 3 hours to restore everything and that was at an Apple Store. (The main reason it took so long was beacause of the large number of apps on the device and the fact that with iOS 6 multiple apps can't download at a time. This means that I had to wait for one app to download and fully install before the next one downloaded.