Is the rak'ah of forgetfulness (sahw) counted as part of the total number of rak'ahs for Witr, or is Witr completed with a separate rak'ah?

If one intends to pray two rak'ahs of Qiyam al-Layl, then mistakenly stands for a third, he must sit down as soon as he remembers. He should not recite the tashahhud again if he already did so. He then performs the prostrations of forgetfulness (sujud al-sahw) and pronounces the taslim. It is not permissible for him to continue the prayer to make it a witr prayer, because he only intended two rak'ahs, based on the hadith: "The night prayer is two by two." If he remembers after starting the recitation (in the third rak'ah), he must return and sit down, then pronounce the taslim, perform the prostrations of forgetfulness, and pronounce the taslim again.