I have a 15" Macbook Pro Early 2011 and OS X 10.9.2. Spotlight is starting to re-index process when I logged in. I want to know: is this a normal behaviour?
Yes, Mac OS X will often index the spotlight at startup. Depending on how many files are on your computer, this process will range from a few seconds to a few minutes (if your computer is terribly slow). I hope this helps!