Why has the Sinai Peninsula historically been a part of Egypt?
It looks like it would naturally be a part of the land area of Israel/Palestine.
Because Israel evacuated it, according to the terms of the Camp David Accords. Begin thought it was worth peace with Egypt, and he was right. This caused a lot of tumult with the settlers and the Israeli right, but Begin was able to pull off a sort of "Nixon in China" thing here.
It wasn't part of Israel until the Six Day War, when they captured it from Egypt. Egypt tried to get it back by force in the Attrition and Yom Kippur Wars. Following the YK War, Egypt and Israel signed an agreement in 1975 stating that they'd solve the problem peacefully, and it mentioned Israeli withdrawal from the Sinai. Sadat was absolutely insistent: even with the political situation in Egypt, without the Sinai, the IDF could be in Cairo in no time. It was completely necessary for Egypt to get it back.