How can I add Wolfram Alpha to search bar in Chrome?

Ultimately I found the solution myself, but it took me some time and I had to devise the solution myself, since all Google searches returned the extension which I wanted to avoid. Here it is.

1. Right click the address bar and click Edit search engines...
   (or open Settings -> Search -> Manage search engines...)

2. Usually, you can find all recognized search engines you used already listed there, but if not, add this: (*use any keyword of your choice)
   

   The query url: http://www.wolframalpha.com/input/?i=%s

Now it is possible to use wa query from search bar to search on Wolfram Alpha. Note, this method allows you to use any search engine.