f=Integrate[6/4*(c2-a2)^2*(s-b1)^2,{b1,0,s}]+Integrate[6/4*(c2-a2)^2*(b1-s)^2,{b1,s,1}];
s=(1-t)*a1+t*c1;
g=Integrate[f*(c2-a2),{t,0,1},{c1,0,1},{a1,0,1},{c2,a2,1}];
Integrate[g,{a2,0,1}]
Integrate[(Abs[(x2-x1)*(y3-y1)-(x3-x1)*(y2-y1)]/2)^2,{x1,0,1},{y1,0,1},{x2,0,1},{y2,0,1},{x3,0,1},{y3,0,1}]