To restore from backup see:
Restore your device from an iCloud or iTunes backup - Apple SupportIf you restore from iCloud backup the apps will be automatically downloaded. If you restore from iTunes backup the apps and music have to be in the iTunes library since synced media like apps and music are not included in the backup of the iOS device that iTunes makes.
You can redownload most iTunes purchases by:
Downloading past purchases from the App Store, iBookstore, and iTunes Store
To determine if y have an iTunes backup go to iTunes>Preferences>Devices and available backup(s) made by iTunes ae listed.
The only way to check if you have an iCloud backup is to on another iOS device signed into the same iCloud account go to Settings>iCloud>Storage>Manage storage