be/have been

[2006]

I don't know what the underlined part means. And present perfect tense does not usually refer to action which has been completed.
I beg to differ, the present perfect is often used to describe something that started in the past, finished recently, and still has relevance at this moment. Using the example of "I have been sick with flu", if someone said to you "I haven't seen you for a while, have you been ill? you could quite correctly say "(Yes) I have been sick with flu".

Yes, you are right; you can say that.
(As an aside, I should also say that in that sentence above one could also say "(Yes) I was sick with the flu."

But back to your main point, I could have expressed myself better.
The underlined sentence was written in the context of the difference between present perfect and simple past, and in that context present perfect is usually used for an action that continues, while simple past is used for an action that is finished.

I have lived in X for six years.
I lived in X for six years.

It seems that is the main reason we have the present perfect tense.