Embed code magic, sir.

<iframe width="560" height="315" src="//www.youtube.com/embed/YQWczN2G4zk" frameborder="0" allowfullscreen></iframe>

Right there at the end of the video code (YQWczN2G4zk), add something along the lines of "?start=XX" where XX is second you want to start at. If you want it to end at a particular time, immediately after that add "&end=YY" where, again, YY is the end second. In the case of this video, it is:

<iframe width="560" height="315" src="//www.youtube.com/embed/YQWczN2G4zk?start=37&end=47" frameborder="0" allowfullscreen></iframe>