Question about facebook intergation

I havent done any research in this topic but would just like to know if its all doable or not. Lets say I have a unity app (webplayer and for mobile). Then I want the user to be able to save the current view as a picture (print screen). Then a button would a appear saying something like "share image on facebook". And when clicked, the picture gets saved to the users facebook albums and appear one the users latest news feed.

I havent used the facebook API or unitys www class so I guess it will be kinda tricky.