How do you solve this calculus question?????? Need help!!!

Question

The question is, let D = integral of (x-2)^3 dx with a range of 0 to c, where c is a constant and 4<c<10. Then express the integral of (x-2)^3 dx of range -c to 0 in terms of D. Here the integrals are all definite integrals** (couldnt show the symbols with my keyboard) also, plz can u guys plz explain why the restriction of c is given??

Answer 1

D is the def integral of (x-2)³ and this integrand is always positive over the integral over (2,10) but is negative over (0,2).

By symmetry, the integral over (0,4) must be zero because the integrand is an odd function.

 

Is this sufficient food for thought?