I agree with the 3rd post here - A Raisin in the Sun is not easily construed as an "integrationist text".
A play about prejudice, poverty, and family, this is not necessarily a play about making social progress through integration. Finding pride in the family is the main challenge for the Youngers. Assimilating into a white-dominated society is not a goal for the family, nor is it easy to find a way to explain the text with this aim in mind.
While race is certainly an unavoidable component of A Raisin in the Sun, I'm not sure anyone can say unequivocally that she wrote this play primarily as an attempt to promote racial integration. As the previous poster points out, the Youngers end up moving into a predominantly white neighborhood, a neighborhood which is willing to pay them not to move. Similar neighborhoods have erupted into violence, and we are invested enough in this family that we hope for the best as they begin a new life. However, in addition to integration, there are plenty of themes about the more general human condition, many of which are not related at all to race. We see rich and poor, American blacks and African blacks, people of good character and people of low character, fears and hopes, discontent and dreams. Integration is only one aspect of this play.
In A Raisin In the Sun, Lorraine Hansberry promotes integration. She does this through the Younger family buying a house in an all- white neighborhood.
Although Mama Younger was just trying to find a nice house for the right amount of money, it just so happens that the house she buys is in an all-white neighborhood.
After deciding upon the house, a man named Karl Linder visits the Younger family. He represents the welcoming committee, but he is not there to welcome the Youngers. In fact, he is there to try and buy them out. The white people do not desire the black Younger family to move to their all white neighborhood.
Hansberry uses this incident to join the races or at least open the eyes of racist people. Although the Younger family is not welcomed to the all-white neighborhood, they decide to move there nonetheless. This story teaches people that there is racism but it can be overcome with perseverance and determination. This book opens the eyes of racist people. It also teaches minorities to stand up for their rights in a peaceful manner.