I don't get why people seem to ignore this. If facebook added internet search to their site they would instantly become the second biggest provider. I would be very surprised if they weren't already working on this.
FB may have Bing search integrated, but its not in any prominent location. I've been on facebook for years and have never seen it, not once. Perhaps its integrated with facebook's people search? The point is, if they put a plain-ol internet search box on each users homepage it will get plenty of use. With the plenthora of data they're generating, internet search can be trojan horsed by way of a history/activity search.