Do the Palestinians want their capital in Jerusalem or "East Jerusalem"?

Reuters makes a practice of referring to the Old City of Jerusalem, the original city of Jerusalem with its treasure of holy sites and historic relics, as East Jerusalem (capital "E").  In so doing, the agency is attempting to manufacture a fictitious identity for a city that has existed for over three-thousand years and was only referred to as "east Jerusalem" following the 1948 Israeli War of Independence and Jordan's invasion, conquest, and illegal occupation of the Old City.  This resulted in a division of the city at the time between western suburbs under Israeli control and to the east, the heart of the ancient city under Jordanian control.  Hence the designation, east Jerusalem.

This distinction has become increasingly important as the Palestinian Arabs seek to obtain sole sovereign control over the city of Jerusalem as evidenced by their many references to the same.  Following then presidential candidate Barack Obama's speech to AIPAC in June of 2008 where he stated that Jerusalem must remain the undivided capital of Israel, Palestinian President Mahmoud Abbas replied:

"This statement is totally rejected," Abbas told reporters.
"The whole world knows that holy Jerusalem was occupied in 1967 and we will not accept a Palestinian state without having Jerusalem as the capital."

And again in January 2010:

Palestinian President Mahmoud Abbas declared on Thursday that Palestinians would not accept any alternative to Jerusalem as the capital of a future state, despite other proposals.
Abbas told Russian television that Jerusalem should not be divided and that there should be free passage for people of various faiths. The Palestinian leader added it must be made clear what belongs to the Palestinians and what belongs to Israel.

Note that while Abbas refers to "East Jerusalem" when commenting on Jewish building there, he is quite clear that it is Jerusalem (full stop) that is being contested:

"If I enter negotiations with them and the building in East Jerusalem continues, Israel will be saying that Jerusalem is theirs. So why would I agree to negotiate while building in East Jerusalem continues?"

The constitution of Abbas' Fatah party also makes clear what the Palestinians are after:

Article (13) Establishing an independent democratic state with complete sovereignty on all Palestinian lands, and Jerusalem is its capital city, and protecting the citizens' legal and equal rights without any racial or religious discrimination.

The repeated reference to East Jerusalem by Reuters and other partisans of the Palestinian cause is simply a fig leaf to conceal the Palestinian objective of controlling the ancient city and its holy sites, leaving Israel with the scraps of the western suburbs.

Occasionally of course, even Reuters miscues:

The Palestinians dream of establishing a capital for their longed-desired independent state in nearby Jerusalem. But that city is fully controlled by Israel and with no Middle East peace deal in sight, Ramallah has rapidly risen to the fore.