Getting a contradiction when integrating a total differential

[Azorspace]

Homework Statement

I'm kind of confused with the total differential, because when i integrate it i get a contradiction, so i wonder if anyone could tell me what I'm doing wrong, please see the attachment to see my problem.

 

[rock.freak667]

dz=(∂z/∂x)dx+(∂z/∂y)dy

∫dz=∫(∂z/∂x)dx+∫(∂z/∂y)dy

which would give z(x,y)= z(x)+z(y) + constant