I said,
"integrate(sqrt(x^2-2*a*x+a^2)*sqrt(x^2-2*b*x+b^2),x);
-> (2*x^3+(-3*b-3*a)*x^2+6*a*b*x)/6
is wrong. I don't know if this is because of radcan but it is hopelessly
wrong"
I should have said that maybe it is wrong in all interpretations, but I
don't know that for a fact.
The right answer, according to the interpretation that sqrt(x^2) = abs(x)
for all real x is, after simplification
abs(x-a)*((x-b)*(2*x+b-3*a)*abs(x-b)+(b-a)^2*abs(b-a))/(6*(x-a))
Rich