I am so confused please help asap! (calc, integrals) please explain as well

A.) 8

Explanation:

Use u-substitution.

(1) Let u=x^3

By the power rule, du/dx=3x^2

Multiplying by dx and dividing by three, we have du/3=x^2dx

To find the new lower bound of integration, plug the old bound, -3, for x in equation (1). We get u=(-3)^3= -27

Similarly, when the upper bound 3 is plugged in, u=27

Now, replacing f(x^3) with f(u) and x^2dx with du/3:

since the value of the first integral of the question = 12, which is given. Although the variable is different than the given (u instead of x), it's still the same integral