My car from last week , started cutting out , seems mainly when engine is cold .  once hot seems to be OK . 
 Just had the VW dealer today do my 40'000 DSG oil change .  when collecting the car , they told me the car cut out a couple of times on them .  they said they believe it to be the fuel sensor and quoted £110 to replace.  I purchased an extended warrenty with them when I purchased the car .
My 2 questions are 
1 ) Are they likely to be right with their prognoses or did I have some bad petrol in the tank 
2 )  Will my extended warrenty cover this.