Vector calc simple question

Been a while since Ive done this but the (unit) normal is (1,1,0), and take the dot with F to get
(y+2x-4)^2
Then for the surface you have y=2(2-x)=4-2x so you can sub that in ...

So would you integrate over x, y and z?
Like z :1-0, x:2-0, y:4-2x? Wouldn’t that get you the volume rather than area?

Edit - just realized the normal isnt quite right in the previous post (thought the face passed through unit values on the axes, but its similar), but when you sub for the y=.. constraint, what is the integrand? Kinda makes the limits irrelevant?

However, youd only integrate over two variables, as you say its an area, and sub a constraint for the third. Subbing the y=.. constriant youd do dxdz where x=0..2 and z=0..1

Oh I see, that makes sense, thanks!