What should the worshiper intend when performing the Witr prayer in which he performs Qunoot: should he intend the Witr or the Qunoot?

Whoever intends to perform the Witr prayer must make the intention for Witr, because it is a specific act of worship that requires an intention to designate it. As for the Qunut of Witr, it does not require a special intention, because it is a type of supplication that one may perform or omit.