Flux across a plane with varying electric field

1. The problem statement, all variables and given/known data
I got home from a test, had an extra credit problem semi memorized and am wondering how I was suppose to solve.

http://i.imgur.com/cIOdSvk.png

A plane with sides [itex]L[/itex] is at [itex]x=3[/itex] . An electric field [itex]E = α y^2 x i + α z^2 y j[/itex] passes through (where [itex]\alpha[/itex] is a constant). Find the flux through the plane. (Givens are [itex] L, \alpha[/itex]


2. Relevant equations

[itex]\Phi = \oint E \cdot dA[/itex]

3. The attempt at a solution

Frankly I didn't feel like I knew what I was doing. The plane varies along y and z and the vector for dA will always go in the i direction

[itex]dA i = dydz i[/itex]
[itex]E \cdot dA = \alpha y^2 x dydz[/itex]
[itex]\int_0^L \int_0^L y^2 x dydz[/itex]
[itex]L \alpha x \frac{y^3}{3}|^L_0[/itex]
[itex] \frac{L^4}{3} \alpha x[/itex]

x=3

[itex] L^4 \alpha [/itex]