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You do have to create the database before you are able to restore to it with MySQL yes but you can do this from command-line along with the restore script as follows:
mysqldump -u [user] -p database_1 > backup.sql
mysql -u [user] -p -e "create database database_1";
mysql -u [user] -p database_1 < backup.sql
Note: Please replace [user] with the username you want to use to backup and restore these databases. If you don't know what this should be - it should likely be root.