Engine bay close-up with multiple hoses and tubes, overlaid ques…

Im talking about the tube just above the "I" in this with the bracket attached to it approx. 2 " above the end. the cylinder im referring to is the one just to the right of the "t" in just. it has a hose that has been cut, what is this part and where does the hose go?

Owner caption April 2013 · Photo 5 of 11