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I actually had damage in the same area on my Integra. As far as the lower piece (called a bumper filler I believe if u look it up on ebay) it actually comes off as one piece. You have to remove your trunk interior and tail lights. There are 2 bolts behind each tail light, and 2 bolts under the lights, behind the plastic. It's takes about 30 min to an hour, to get everything apart depending on the car. You could either take that filler piece off, and try taking the dent out yourself, or you could replace the whole thing. The trunk, you'll have to take off the interior, and see if you can get something inside to push the dent out. Or you could replace the trunk lid.
Depending on your location, you may find a mobile dent repair person. They are really good at massaging the metal back into place. If you are lucky and there is no crease in the dent, you can pop it back up from behind. You/they may have to drill an access hole to get past the layers of sheet metal. Or they can use the tool the uses hot glue to pull it back up from outside.
Whatever you do, try not to beat it up with metal objects, you will never get it flat again.
There is always the option of sand, bondo filler, repaint, but it's best to pop it out if possible.