kill(all)$

van=facebook.com/LearningCalculus$

A:matrix([1,1,0,0],[1,0,2,0],[1,1,1,-1],[0,1,0,-1]);

B:matrix([9],[15],[0],[-11]);

fruits:first(linsolve_by_lu(A,B));

integrate(fruits[1][1]*x^2-
          fruits[4][1]*x  +
          fruits[3][1],
          x,
          fruits[2][1],
          fruits[1][1]);