You have to build a "research improvement" on a tile with a research bonus in order to reap the benefit of that bonus. You will see that bonus reflected in the "level" of the improvement once it's built. The same is true for all other similar bonuses.

You can see what level a structure is going to be when you put down the plan to build it, so you don't have to guess. Try building a research improvement on a tile with a research bonus and you'll see that the projected structure is going to list a higher level corresponding to that bonus, even before the improvement is actually built.

Also remember that second bonus is for the improvements next to it. This will probably conflict with you research adjacencies. You decide which is more important.