Yes, sorry, I was thinking of the partition editor in another distro. I think you will have to do it the hard way:
In a terminal type blkid, this will give a list of all your partitions with their UUID's.
Make a note of the UUID of your new partition, /dev/sdb1 (without the quotes)
Now right click on the file /etc/fstab and open it as administrator.make a backup copy by doing Save As and calling it fstab.old just in case you mess things up.
Now add the following at the end of the file:
UUID=(the number you noted) /Backups ext4 defaults 0 3
followed by return
Then save it as fstab.
Now reboot and you should have your new partition mounted as /Backup
Laptop: Toshiba Satellite C870 13V . Mint Cinnamon 17.1
Desktop: Gigabyte GA-MA770T-UD3 motherboard, NVIDIA GeForce 210, AMD Phenom II Quad Core Processor 3GHz, 4GB ram, 120GB SSD, 500GB HDD. Mint Cinnamon 17.3