Is East Jerusalem part of Israel because I m confused I thought most countries that recognize Palestine recognize East Jerusalem as the capital of Palestine ?
No it is not. It is part of the Occupied Palestinian Territories.
From the end of the “conflict” between Israel and the Arab states in 1949 until 1967, the city of Jerusalem was divided - the western half controlled by Israel, and the eastern half under Jordanian rule.
In the June 1967 war, that Israel started, Israel seized the eastern part of Jerusalem, along with the rest of the West Bank. The Old City of Jerusalem, bounded by a wall, and holding the most important religious sites to Jews, Muslims and Christians, was in the eastern half of the city.
After the 1967 war, Israel extended its law to East Jerusalem - in effect, annexing it - and also progressively expanded the municipal boundaries of the city, incorporating the lands of 28 villages in the West Bank. Israel's changes to the juridical status of Jerusalem have been deemed violations of international law by the United Nations Security Council, as have its illegal civilian settlements, both in Jerusalem and other parts of the West Bank and Gaza Strip. Today there are over 450,000: Number of Israeli settlers living illegally on occupied Palestinian land in the West Bank. (Additionally, there are more than 225,000 Jewish settlers living illegally on occupied Palestinian land in East Jerusalem). Approximately 11,000 of the settlers in the West Bank are located in the Jordan Valley. Additionally, over 25,000 Israeli settlers live illegaly in the occupied Syrian Golan Heights. There are 279: Number of official Israeli settlements built on occupied Palestinian land in the West Bank, an area smaller than the state of Delaware. There are also 147 so-called settlement “outposts,” or new small settlements built without official approval but with the support and assistance of the Israeli government. While Israel evacuated some 8,500 settlers from the Gaza Strip in 2005 to freeze the peace freeze the peace process , some simply moved from illegal colonies there to equally illegal colonies in the West Bank and East Jerusalem.