What's the name of the song  Maya Angelou quoted at the beginning and
end of her speech at the funeral for Correta Scott King?

Maya Angelou began and ended her tribute to Coretta Scott King with a
quote from the spiritual song "I Open My Mouth."

"MAYA ANGELOU: [singing] I open my mouth to the Lord, and I won't turn
back no. I will go. I shall go. I'll see what the end is going to be.
[speaking] In the midst of national tumult, in the medium of
international violent uproar, Coretta Scott King's face remained a
study in serenity.

. . .

I pledge to you, my sister, I will never cease. I mean to say, I want
to see a better world. I mean to say, I want to see some peace
somewhere. I mean to say, I want to see some honesty, some fair play.
I want to see kindness and justice. This is what I want to see. I want
to see it through my eyes and through your eyes, Coretta Scott King.
[singing] I open my mouth to the Lord, and I won't turn back. No I
will go. I shall go. I'll see what the end is going to be. Thank you."

Democracy Now: Last Tributes to Coretta Scott King
http://www.democracynow.org/article.pl?sid=06/02/08/1516213

In case you're interested, here are more lyrics:

"I Open My Mouth (I Won?t Turn Back)

Done made my vow to the Lord 
O, Lord, I?ll never turn back. 
I will go! I shall go to see what the end will be.

I open my mouth to the Lord, 
And I won?t turn back. 
I will go! I shall go to see what the end is gonna be.

If you don?t believe that I?ve been redeemed, 
Just follow me down to Jordan?s stream.

I open my mouth to the Lord, 
And I won?t turn back. 
I will go! I shall go to see what the end is gonna be."

Wednesdays at Eight: Let Me Fly! Songs of Spirit
http://users.usinternet.com/mmuller/wednesdays_at_8/docs/Concert3Program.pdf

My search strategy: I had bookmarked the "Democracy Now" page several
days ago because I found the services to be very moving, and wanted to
keep a transcript. Once I had the name of the song that was quoted by
Dr. Angelou, I used this Google search string to find additional
lyrics:

Google Web Search: "i open my mouth to the lord"
://www.google.com/search?hl=en&q=%22i+open+my+mouth+to+the+lord%22

I hope this is precisely what you need. If anything is unclear or
incomplete, or if a link doesn't work for you, please request
clarification; I'll gladly offer further assistance before you rate my
answer.

Best regards,
pinkfreud