Ikeep getting my answer as a = 7 and b = 63, but i am also wondering about a = 8, b = 64. i would love to get a second opinion before i put down d as my answer.

Yes, a = 7 and b = 63 is the correct answer.



we're given that 
 
   

looks like a u-substitution was made with u = x³ - 1.
so if u = x³ - 1 then

   

but we also have to change the limits of integration. those limits were in terms of x-values; now we need to change those limits in terms of u-values.

in terms of u:

    u(4) = (4)³ - 1 = 63
    u(2) = (2)³ - 1 = 7

doing the substitution for the left-side including changing the limits of integration:

   

you could always confirm these types of questions with a graphing calculator. i've attached a picture from desmos of what i used to confirm my answer.

both integrals have the same value.

It is e) i am not sure if you have any questions or need any