Charley asks a good question: "Why is that indentation there?"
When we bought our house (built in 1913), there was a sunken area under the stove. Turned out termites had damaged the joist under it. The problem was easily fixed with a sister board in the basement, but if we hadn't fixed that, the floor never would have stayed level.
(Never believe the people who tell you that the important thing about a house is "Location, location, location."
And when people say "They don't build 'em like they used to," I answer, "Thank God for that.")
On the other hand, it could be something simple, like that something very heavy once stood there. If that's it, I would just go to a hardware store and ask for advice. There could be a nifty new product that will get you fixed up in no time.
I put down self-stick floor tiles maybe 8 years ago, and they still look great. I'm glad I did it.