Twitch integration is coming to Xbox One tomorrow, and you can watch pretty much every bit of it above in Microsoft's newest video. Basically all you need to do is sign up for an account on www.twitch.tv, then go to your settings and archive broadcasts.
Then just open up your share preferences, and you're good to go. Although this update is late, it's great that every single Xbox One owner will be able to use this to its full potential given that everyone has a Kinect.
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