Calibre itself gives you a link down in the bottom right of the screen where it tells you to update. Or just go to the main calibre
download page...
Your books and library will be absolutely fine. There are times when you upgrade calibre it needs to make some updates to the library database, so you can go "forwards" in versions but not backwards. If ever in doubt, make a backup of your whole library folder before you upgrade (but you should be keeping backups anyways).