What's in the two black boxes at the bottom right, next to the intake?

 

my guess is fuses in the smaller box

 

Yeah, the owners manual seems to indicate that the fuses are in there.

What about the closest one? It's got a picture on the top of a book, like it wants you to check the manual or something.

 

Its the ECU


B

 

That fusebox contains mostly the high current fuses and relays used by the engine control, power steering, ABS, etc. A second fusebox in the drivers footwell contains several dozen more for the accessories.

The ECU of course is the engine controller. There is another one in the passenger's footwell that is responsible for all the body and accessory functions.

For a small car, the MINI has a very involved and sophisticated electrical system!