I think that the right hand side must be 4xy(x2-y2).I nudged u the same but u said that the question is absolutely correct.But I still think it is so,b'coz then It can be solved as follows
(x-y)f(x+y)-(x+y)f(x-y)=[(x+y)2-(x-y)2](x+y)(x-y)
This gives f(x)=x3,just by comparing both sides and hence the two curves are
y2+x=0 and x2+y2=12 which are a parabola and a circle.
Thus,The area can be calculated by finding points of intersection and applying corresponding integrals.
MAKING A MISTAKE IS HUMAN BUT REPEATING IT IS IDIOTIC.
allamraju very very true i totally accept u corrected the RHS i adjusted the LHS i have did this q before the sol is f(x)=x^3 that's what i nudged him but he says the q is perfectly correct i dont know...