My version of LibreOffice is 22.214.171.124. and 4.0.3 was released three days ago.
Should I add PPA in order to get updated or my Ubuntu 13.04 will update automatically after few days?
I would wait a while before upgrading just to see if there are any issues from such an upgrade. But to do the upgrade you would just press Ctrl+Alt+T on your keyboard to open Terminal. When it opens, run the command(s) below:
Before the upgrade
After the upgrade
Or you can just wait, and it will be upgraded automatically.