Where (>0) does y = c intersect y = 2x-3x^3? If the answer to that is x=D1 and x=D2, then you'll need two integrals, one on [0,D1] and another on [D1,D2]. Where did those values come from?
I dare say c is in [0,(4/9)*sqrt(2)]. You tell me why.
Have you been introduced to the concept of finding the area between two curves?