To be honest, the only way to truly make every piece of data on a old drive un-recoverable and un-readable is to take the HDD apart, and break the disks, and just mess them up real bad.
However, this does not seem to be what you want to do, as you only want to remove the data from a certain partition of a drive you still want to use. Another, albeit impractical, option, would be to refill that entire partition, or really the whole drive, with large files that contain nothing important. This would write over any "good data" with the random files.
Basically, what I am getting at is that there is almost no way to make data unrecoverable from a drive you still want to use. An HDD will not, and cannot (I believe), delete data. Only remember what space on the drive has been deemed "unused" when you delete files that existed there. If it needs to write something new to the drive, it can then write over the old data with the new data. But there will still be data on the drive, even if that data is nothing important.
However, I assuming you just simply want the data that was there to not be findable by you accidentally, then yes, you can just use that option, or you can do what I like to do, and go to Disk Manager, where you can delete, and then re-create, the partition. This removes access to any data there by a user or program. It is still present on the drive, however, until it is written over.