The boundaries of the city shall be the same as have been heretofore established and now exist and those boundaries established and changed hereafter in all annexation and disannexation proceedings of the city, filed in the office of the city secretary.
   The city council may by ordinance annex territory adjacent to the city with or without the consent of the owners or inhabitants of the annexed territory and subject to the procedural rules subscribed by the laws of the State of Texas. The City Council, after a public hearing and a majority vote of the council, may, by ordinance pursuant to State law and this charter, disannex any property lying within and adjacent to the boundary limits of the city and lying adjacent to the city limits.