When you finish with customs (after collecting your bags from the luggage belt), you will need to recheck them. This is really simple and basically involves turning them back in to the airline after the customs check. You will not need to haul them to the ticket counters in the UA terminal. Also you will go through security after transfering to the UA terminal at LAX. Don't forget to put any dutyfree liquids you might have purchased (non-liter zipbag contained, regardless of what they tell you or package them in SIN) into your checked luggage before turning them back in to the airline, as otherwise TSA will take them.