At the time and place fixed in the notice, the board of supervisors shall meet for the hearing of the objections. If it finds that due notice has not been given as required by section 31-324, it shall continue the hearing to a date to be fixed by the board, and order the publication of the notice as hereinbefore provided. When the board finds that due notice has been given, it shall proceed to hear any objection or objections that may have been filed upon which an issue has been made, and for that purpose shall have the power to subpoena, swear, and examine witnesses, and to do all things necessary and incidental to a proper hearing and adjudication of such issues. It shall examine the maps, profiles, plans and report of the engineer, the items of the estimated cost of the drainage improvement recommended, the classification of the land and property in the district, and the assessment of the benefits to the same as proposed by the engineer. The drainage board shall also have the power to establish the classification of the lands and property, and to determine and adjudicate, the total amount of the benefit that will accrue to each lot, tract, or parcel of land or other property in the district, from the drainage improvements. Whether an objection is sustained or overruled, the board may modify the report in any particular; but if the objections are overruled, the board may approve and confirm the report as to the property affected, and if it finds the classification of assessment of benefits to the lands and other property to be in any respect inequitable, either less than or in excess of the benefits accruing to the lands and property from the drainage improvements, or in any particular unfair and unjust, it shall so order, shall thereupon so amend, adjust and equalize the classification and benefits as may appear fair, just and equitable to them. When the board has adjusted, equalized and determined the classification of, and assessment of total benefits to the lands and other property as above required, it shall enter an order confirming the same. All pleadings and other papers filed in the matter of such hearings shall be filed with the secretary of the board of supervisors. Subpoenas and other process shall be issued by the secretary, who shall be empowered to administer oaths to witnesses, and to certify to records and papers under the seal of the drainage district.