Surface Integration

The original question:
http://i191.photobucket.com/albums/z...988Surface.png

So far I know it has 4 surfaces and only the bottom face will have -k.

I thought of breaking it down by
S1: Front Face
S2: Left Face with points (0,0,0), (1,0,0), and (0,0,1)

S3: Right Face with Points (0,0,0), (0,1,0) and (0,0,1)

S4: The bottom face

Thanks,
Evan

From the plot I think I found that:

http://i191.photobucket.com/albums/z...ter/3DPlot.png

z=1-x-y

S1) Has points (1,0,0), (0,1,0), (0,0,1) Plane Equation Becomes -x-y-z=0

S2) Has points (0,0,0), (1,0,0), (0,0,1) Plane Equation Becomes y=0

S3) Has Points (0,0,0), (0,1,0), (0,0,1) Plane Equation Becomes -x=0

S4) Has Points (0,0,0), (1,0,0), (0,1,0) Plane Equation Becomes -z=0

any idea what the next step should be?

Anyone know if S2 and S3 should yield an answer of 0??