The curbing in the city shall be built, repaired, or rebuilt in the manner and within the time prescribed by the governing body, which shall order the work to be done by such person as it may have contracted with therefor, under the direction of the city engineer, or street commissioner, if the city has no city engineer, at the expense of the lots or parcels of land benefiting from the curbing. Such expense, including the expense of all notices in connection with such work, the assessment therefor, and any other expense incurred for such work, shall be assessed by the city engineer, or by the street commissioner if the city has no city engineer, against the lot or parcel of land properly chargeable therewith. Such assessment shall be returned by the engineer or commissioner and filed in the office of the city auditor, and the city auditor shall cause the assessment, together with a notice of the time when and place where the governing body will meet to consider the approval of the same, to be published once in the official newspaper of the city at least ten days prior to the meeting of the governing body to consider the approval of the assessment.