I write some code, then I build it (compile it) then I run the tests. This happens on my local machine. That's the "code & build" phase in that diagram.
Then I check my code in to a central repository, triggering a remote build and remote testing. I have now performed a "doesn't just work on my machine" test. I've "integrated" my code into a central repository, thus it's the "integration" phase.
Ultimately though, a lot of this is just semantics. A great many IT processes still refer to the entire "code, compile, test, repeat" cycle as "build". The diagram you link to doesn't show testing on the local machine, nor does it show "build" on the build server.
So take such diagrams with a pinch of salt and don't lose sleep over them. If you feel you are "missing something" when looking at such a diagram, just remember that it'll likely boil down to you using a slightly different semantic model to describe such things to what the author has used.