I am trying to understand this proof (problem 2 pages 1-2) which shows that if a rectangle can be tiled by smaller rectangles each of which has at least one integer side, then the tiled rectangle has at least one integer side.
I can't seem to understand why "the integral of $f$ over any horizontal or vertical line segment with integer length is zero.". How can this be proven mathematically? Could someone help me with the proof linked?