You shouldn't need to ask: if you're booked as a connection, then the default position should be that the bags are through-checked to the final destination.

As always, it's worth checking the bag tag receipt before you leave the counter to make sure that the flights and dates are correct (although I would be the first person to admit that I don't consistently do this myself). If the bag tags are correct, then the overwhelming chances are that the bags will fly with you as planned.