1. Before the city council shall be authorized, under the provisions of sections 88.507 and 88.510, to grade or pave any alley, or to grade, pave or gutter the roadway part of any street, when the improvement is to be paid for with special tax bills, they shall, by resolution, declare that they deem such improvement necessary to be made, and shall cause such resolution to be published in some newspaper printed and published in the city, for two consecutive insertions in a weekly paper, or seven consecutive insertions in a daily paper, and if a majority of the resident owners of the lands that would be liable for the cost of the improvement, at the date of the passage of the resolution, who shall own a majority of the front feet owned by residents of the city, abutting on the street or part of street proposed to be improved, shall not within ten days after the date of the last publication file with the city clerk their protest against such improvement, then the council shall have the power to cause the improvement to be made; and if the council shall find and declare by ordinance that no such majority have so filed such protest, such finding and declaration shall be conclusive, after the execution of the contract for the making of the improvement, and thereafter no special tax bill shall be held invalid for the reason that a protest sufficiently signed was filed with the clerk.

2. The council shall have full power to make all provisions deemed necessary for the making of contracts by the city, for the doing of all the work necessary in making the improvements herein specified, but all such contracts shall be let to the lowest and best bidder, upon advertisement for bids, published by two consecutive insertions in a weekly paper or seven consecutive insertions in a daily paper in some newspaper published in the city.

3. But before the city shall make any contract for any of said improvements excepting repairs, an estimate of the cost thereof shall be made by the city engineer, and in case there be no city engineer, such estimate shall be made by some other person designated by ordinance. Such estimate shall be filed with the city clerk and no contract shall be made for a price exceeding such estimate.

4. The council shall have the power to require any contractor doing work to guarantee that an improvement will last for a specified term of years, and during such term will be kept in repair, and to require the contractor to give to the city approved bonds for the faithful performance of any obligation.

5. The council shall have the power to repair any sidewalk, curbing, guttering or paving without letting any contract for such work, but can have such work done in such manner as may be provided for by ordinance. When such work is done by the city, not through a contractor, the tax bills shall be issued to the city and the city shall have the same power to collect such tax bills as other owners of tax bills.