Area from a definite integral

I am suppose to obtain an area bound by 3x + y = 6 above and below by y = x^2 - 4 and the y axis. I think I should take the integral of the first and subtract the integral of the second one from 0 to 2

In terms of x: 6x - 3x^2/2 - (x^3/3 + 4x) from x = 0 to 2. Am I on the right track on this one????? Please let me know. I asked someone else in my class and they added the two integrals and used |x^2 - 4| for second integral?? Thanks again for this wonderful site!!!! Frost King