That depends upon what the lease agreement says. Due to the rising cost of heating an apartment, you must pay close attention to the part of the rental agreement dealing with utilities. You can contact the utility company and ask about last year´s cost and the projected rate increase for that unit. It is not wise to rely solely on the information your landlord provides concerning utility costs.
In Lincoln, city law requires the landlord to provide for the collection and removal of garbage at least once a week. See Lincoln Municipal Code 8.32.205.
If the landlord is to assume the cost of particular utilities, make sure this promise is included in the lease. If you make an addition to the lease, have your landlord initial it.