The governing board of any institution which has heretofore issued or which hereafter issues bonds or notes pursuant to the authority of Article VII, § 17, of the Texas Constitution, as amended, may issue refunding bonds to refinance or refund any or all of the bonds or notes by the issuance of its refunding bonds; and the governing board may pledge all or any part of the funds allotted pursuant to that section of the constitution to any institution governed by the board to secure the refunding bonds issued pursuant to this section. The refunding bonds shall be issued in the amounts, and bear interest at the rates, determined by the governing board, provided that such interest rates shall not exceed any constitutional limit; and shall mature serially or otherwise in not more than 10 years. The refunding bonds shall be examined and approved by the attorney general, and when so approved shall be incontestable, and all bonds shall be registered by the comptroller of public accounts. The refunding bonds may be exchanged for bonds or notes issued pursuant to the section of the constitution or may be sold and the proceeds used to call and redeem the outstanding bonds and notes.