It's from Family Search.
You need to be a signed on member (it's free and takes only a couple of minutes to join. Well worthwhile!).
You will not find it on a general search on Family Search, which is the case with many of the records they hold.
You have to search the catalogue for the relevant place, in this case Benfieldside, then look at the cemetery records page by page. Fortunately I knew where to find the cemetery records as I've used them many times before.
Having found the newspaper announcement it was easy to find the relevant page of the register.
The burials are also transcribed on Durham Records Online, but I like to see the original.
