Did blacks want integration?

Whenever I watch or read programs about the fight for civil rights in the 1960's, they always portray people marching in support of school integration. My question is, did black people at that time really want to integrate public schools? I can vividly remember large groups picketing outside my school, but they were chanting "Hell, no - we won't go!" Meaning they did not want to leave their school. This confuses me. Can someone who knows a lot about that era and the civil rights movement explain the conflict between my memories and what is written in the history books? Also, I have friends that went to school at that time in Long Island, New York, who told me that there were no black students in their school the whole time. Did integration and busing only apply to the southern states? I am not trying to sound racist, just want to understand more about that period of US history. Thank you.