Why is the flux through the top of a cylinder zero?

[Sam Anderson]

This is example 27.2 in my textbook. I have the answer, but it doesn't make sense to me. I understand that if electric field is tangent to the surface at all points than flux is zero. Why, though, does my textbook assume that the ends of the cylinder don't have field lines extending upwards and downwards, out of the top and bottom of the cylinder?

 

[Seydlitz]

What textbook? It's important to know what kind of charge distribution you have inside the cylinder and how it's positioned.