back bumper repair or replace it

Very difficult to say without seeing it in person. There is a support structure behind it that may also need repair as well as repairing or replacing the bumper cover. The color of the vehicle also enters into it as some colors are very difficult to match so you end up doing a lot more work to blend the new paint into the original color.
I would start by talking to the insurance company, then ask your local friends for recommendations of shops that can do the repairs, don't overlook a dealer, they are usually a bit higher in price than an independent shop, but not always. Get a few estimates, be sure they are for the same work and parts though, for instance if you want the cover replaced with new or used OEM then be sure that is the same in all. It may be cheaper to replace the cover than repair it so be sure the estimates cover everything. The attached show the parts that may be damaged, the support may be damaged even if it looks like it's only the cover.

Thanks Mr.Steve. here is a picture. I think the only thing that needs to be repaired is the rear bumper and the rear lower bumper it was not a big hit, but it is still visible.

That might be able to be buffed out if it's only the clear coat that was damaged. Doesn't appear to have torn through in the color area below the back-up sensor. If that is possible or even just scuffing it and shooting on new clear it would be a much simpler repair. Shops in my area would likely heat the spot with a heat gun to push it back into shape, then see what the extent of the paint damage is. If they could do just a couple small touch up spots and new clear I would say around $400.00 to $500.00 as a start. For the bottom edge it is easier as that trim color is an easy one to match.

Thank you so much you where a great help. One question I do have is, that I think I might have to pay more than that due to the fact that it is broken or cut in these two areas.

Maybe, it would depend on the shop. They both are easy repairs. The question then is how good the shop is and if they would repair the part. Some will some won't. The upper one is actually the bad one as it is in the color area. That could be repaired and the spot touched up if the shop knows what they are doing it would be barely noticeable. Really depends on the skill of the one doing the work.
The lower one is much easier as that color doesn't match the panels next to it so you could repair it and paint it and a minor mismatch wouldn't be noticed because the next panel of that color is on the other end of the car.

Or you could do like the locals here do and stick a bumper sticker over it and call it good, LOL.

Again thank you so much for your help. I appreciate so much you really helped me with this problem.

You are welcome. Please return anytime, we are here to help.