Concept:Use the property of odd functions over symmetric limits to simplify the definite integrals.Explanation:Given ∫abx3dx=0. So [4x4]ab=0, which gives b4−a4=0. Thus b=a or b=−a. Since ∫ab(x2−x)dx=18=0, b=a is not possible. Hence b=−a, meaning the limits are symmetric about 0. Now ∫−aa(x2−x)dx=∫−aax2dx−∫−aaxdx=18. The integrand x is odd, so ∫−aaxdx=0. Therefore ∫−aax2dx=2∫0ax2dx=2[3x3]0a=32a3=18. This gives a3=27, so a=3 and b=−3. Thus a+b=3+(−3)=0.Answer:a+b=0, hence the correct option is C.