Help my sink is leaking, backing up and I'm confused

Okay I understand what a trap is and the water goes down the drain into this pipe and pipe goes into the wall... that connection is fine...

But why do I have a second pipe line that is silver then runs upwards turns copper and is cut off into nowhere... the water is pouring out of there when ever my water gets more then an inch in my sink...

What is this supposed to be connected to?? Or capped off with...
Why is this happening

The people who installed my dishwasher and new garbage disposal insist that it is all hooked up right but what is going on??

It is hard to visualize your plumbing hook up. Is it Dishwasher related ? Can you snap a picture of it and post it here ? Back to you...

Yes it is hooked up to the dishwasher I don't know how to post pictures yet but if it helps any...

There are two pipes that come out of the wall and one is hooked up to drain the sink but the other one is spouting water out of the top... it isn't

Connected to anything it is just cut off and I don't know if it can be capped off or needs to be connected somewhere to drain... the water from the sink and dishwasher will come out here if it backs up