It is the crankcase breather hose. The funny plastic box is the oil trap.
You really should replace the hose as it will allow unfiltered air into the engine/crankcase. I doubt the OE part is very expensive, but you could make one out of any breather hose of the correct diameter from Halfords or your local motor factors.
The genuine hose is �8.55 -
http://www.yamahaMotorcycleSpares.co...11670000&uid=0