Mysql databases can be backed up by doing the following:
- Go to 'backup', under the 'Site Management' header in cPanel.
- Underneath where it says "Download a SQL DB Backup", click on the database name that you wish to backup
- Select a place and filename for you to save on to your local computer
- Do NOT attempt to open this file with Winzip.
You have now sucessfully backed up your MySQL database with cPanel.