There's a webpage that was just updated a week ago. But now I can still google what was present in that webpage before it was updated, and Google says that result/webpage was from 2 months ago. I wonder why?
Google (and, honestly, all search engines) does not instantly index every single web page in its database. Using whatever their proprietary analysis determines, they'll eventually get around to re-indexing the page. For pages that Google knows are updated frequently, it will check more frequently. For others, not so much.
There used to be a tool you could use to alert Google to an URL that had changed, but they've admitted that they don't pay much attention to it, if it's even still up. (There is, however, such a tool available in their Webmaster Tools that they do pay attention to.)
Since the page is in Google's index, they will eventually get around to re-indexing it.