There are two methods for taking backup of a single table from a database and restore in into another database
In this method you can take a backup of a database table and restore into another db. But this restoration will remove the already existing table and recreate it in the new database .
# mysqldump old_db table > old_db.table.sql
# mysql new_db < old_db.table.sql
In this method you can table only the backup of database table data ( not the sql scheme ) and restore it into new database without removing the old data in new database
# mysqldump -t old_db table > old_db.table.sql
# mysql new_db << old_db.table.sql
Make sure to table backups of new database before doing the restoration