"Allah—there is no god except Him—is the Living One, the All-sustainer. Neither drowsiness befalls Him nor sleep. To Him belongs whatever is in the heavens and whatever is on the earth. Who is it that may intercede with Him except with His permission? He knows what is before them and what is behind them, and they do not comprehend anything of His knowledge except what He wishes. His seat embraces the heavens and the earth and He is not wearied by their preservation, and He is the All-exalted, the All-supreme. There is no compulsion in religion: rectitude has become distinct from error. So one who disavows fake deities and has faith in Allah has held fast to the firmest handle for which there is no breaking; and Allah is all-hearing, all-knowing. Allah is the wali of the faithful: He brings them out of darkness into light. As for the faithless, their awliya are the fake deities, who drive them out of light into darkness. They shall be the inmates of the Fire, and they will remain in it [forever]." - Qur'an 2:255-7
Yes, the two verses are included because many of our leading Scholars relying on authentic Hadeeths say that according to precaution, Ayatul Kursi is three verses ending with Khalidoon.