Restoring Post Backup

Hi, I recently moved hosts and I didn’t want to mess with trying to restor the whole database so I just did the backup plugin that comes with WP. I’ve read through the docs on wp.org and cannot find for the life of me how I can just restore that backup. All the docs talk about using phpmyadmin and restoring the database which I do not want to do. I just want to restore the old posts…Any help?

Thanks