I updated the wording to make it more clear how the bonus impacts your teching.

It works by displaying it in the following format (Example assumes I have 65 turns):
You can research 15 technologies per turn (+3 technologies per turn for the next 10 turns). You have time to develop 1,005 new technologies.

So the 1005 technologies I can develop is equal to 15*65 + 3*10 = 975 + 30 = 1005

Hopefully that is more clear now :)
When you don't have the teching bonus active, it will not show.