Simple script to backup a MySQL database and delete files older than two days:

mbak.sh

#!/bin/sh

bkpdate=`/bin/date +%Y%m%d-%H`

/usr/bin/mysqldump --user=root --password=yourpass --lock-tables=false --databases list_dbs_here > /databases/backup-${bkpdate}.sql
/usr/bin/zip /databases/backup-${bkpdate}.zip /databases/backup-${bkpdate}.sql

for file in "$( /usr/bin/find /databases -type f -mtime +2 )"
do
  /bin/rm -f $file
done

exit 0