There are two type of LED tube to replace florescent tube:

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First figure is florescent using electronic ballast whatever. This one shows the LED tube that has single end connection

The second figure, which is more common, is using both ends of the LED tube.

Normally there is diagram that come with the tube so that you know which connection is to be used. For connection that used both ends, you can connect to either pin of the tube at each end.

Should look like this in your case. Capacitor not really a needed. Just optional. Probably the magnetic ballast/choke inside really poor that's why.

You asked a proper electrical shop ? A bakery shop owner sure blur blur !

Forget about the capacitor. The capacitor is for suppress the noise from the florescent light. Also called EMI capacitor. It is under safety class capacitor. It is designed to open circuit when failed. Traditional circuitry is more conservative and new design is to reduce cost 

For LED, it is not needed since you do not have starter that create spark, thus noise.

u should thank ur developer/whoever installed it for not being a cheapskate
all these 25y u're enjoying almost 1/2 saving for that light compared to not using capacitor