You can do this by adding an extension to the URL.

Example: 

http://www.youtube.com/v/XGSy3_Czz8k

adding extension  “?start=60” for starting point  “?end=120” for end point

 http://www.youtube.com/v/XGSy3_Czz8k?start=60

for more useful parameters You Tube Documentation  

 

 

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