What is involved with replacing floor joists
Working from the info you proide:


Back up 6 feet from the wall.
Put a 5 foot chunk of 2x10 against the ceiling spanning the bad joists and good ones on either side.
Put another chunk of wood, 3/4 ply or osb on the floor to protect the floor. (If you have ceramic tile on the floor figure out a way to spread the load.)
Put in 2 teleposts. and take up the slack.  You aren't supporting anything.  You are just keeping the teleposts from falling over.
On a wall far enough from the problem to be stable, put a shelf, about 18" from the ceiling.  
Rest a laser level on this shelf.
attach  16" chunks of wood to the 3 bad joists and the good one on either side.  You want to measure the middle of the board, and the ends that are on good joists.  These chunks need to be line of site to the laser level on the shelf.
Affix a cheap ruler to each board.  Record the ruler marks in your notebook.  This is how you are going to check what hapens.
Now, in the basement: Set up a similar support beam and pair of teleposts.  This might be overkill. 
Set up a similar shelf and indicator for the joists under the
upstairs telepost. 
Tighten the upstairs teleposts enough to get detectable movement on the center indicator.
Go downstairs and see of you are pushing the floor down.  If so,  tighten up the downstairs ones to bring it back up to the original reading.
Back upstairs.  Gradually lift the board, until you have motion on the good joists.  Back off a bit. 
Back downstairs.  Check that the floor hasn't pushed down.


At this point you have the good part of the joists level with the rest of the ceiling, and the load isn't bending the lower floor out of shape.


Now you can cut the bad joist back to good wood, or at around 4 feet.
use an angle grinder and take off the ends of nails and screws poking into where the joist was.
Clean out the hole.
Insert new chunk of joist.  If you haven't addressed the problem that caused the rot, use pressure treated wood.


At this point I'm of two minds.  You need to splice the new chunk to the old chunk.  My gut level feeling is that I want a 6 foot chunk lapping the joint on both sides.  There's going to be significant stress on the fasteners.  I think I would use both glue and 2.5 inch x 5/15 lag bolts.  

This is where you should consult someone wiser than I am.  I'm not sure how many bolts you should use or what the spacing should be.  Without a consultant I would put two rows of bolts 8 inches apart, alternately 1 inch and 2 inches from the edge.  Bolts from the other side have the opposite alternation and are offset 4 inches so that in the middle joist there are no bolts closer than 4 inches, and no two adjacent bolts are on the same grain line.

At this point you should be able to take down the teleposts and not have anything move much.  

Caveats:  I've not done this.  I am not a professional.