Q: Where are the podcast found?

If you restored from a backup, these Apple a Support articles on how the backups work and what items are backed up, will help ...

Choosing an iOS Backup Method (Should I Use iTunes or iCloud to back up ...)

https://support.apple.com/kb/HT5262

Back up and Restore your iOS Device with iCloud or iTunes

http://support.apple.com/kb/ht1766

iTunes: About iOS Backups

http://support.apple.com/kb/ht4946

Create and Delete iPhone, iPad and iPod Touch Backups in iTunes

http://support.apple.com/kb/ht4946

iOS: Troubleshooting Encrypted Backups

http://support.apple.com/kb/TS5162

Have you downloaded the Podcast app?

Nevermind