Help me with Surface intergral!

Homework Statement

Evaluate $$\int$$$$\int$$ (x^2 +4y + z)dS where S is the portion of the plane 3y +2z = 6 with 0<x<3

Homework Equations

choosing x, y as variables
dS = $$\sqrt{}(partial dz/dx)^2 + (partial dz/dy)^2 +1$$

The Attempt at a Solution

If i choose x, y as variables or x, z as variables, then when i choose limit of intergral, x will go from 0 to 3 whereas y or z will go from -infinite to +infinite, and solving the intergral results of infinite result (seem to be not right to me)
if choosing y,z as variables, then i can't "translate" f = x^2 + 4y + z into parameterized f since x does not depend on y and z in the plane 3y +2z = 6 (in the common problems, the plane involves x, so i just forming x = g(y,z) and then sub x into f which is in the intergral)
Any help would highly appriciated.