Plumbing and Piping - Strange pipe under sink

Hello. I've just recently purchased an older Home and I am finding little rigged up things throughout the house. The oddest thing is this strange pipe hookup under the sink. I have a dual drain sink. Underneath the two drains go into one pipe that is not hooked up. It just drips/flows down the pipes and into the small trashcan that is now under the sink. I need advice on how I should replace this. I don't know if I should either replace the unattached pipe or replace the whole assembly.
Thanks,
keschra

keschra:
You need to determine why the plumbing was disconnected in the first place and whether or not it ever worked.
Is talking to the former owner a possibility?
You could hook it up and see what happens.