How does sweeney todd end?

Todd finds out that the crazy beggar woman that he killed was really his wife Lucy and discovers that all of the things that Mrs. Lovett had told him about her were lies. So he starts singing about how to forgive and forget, they start spinning and dancing and he throws her in the oven. Then Sweeney goes over to Lucy's dead body and cradels her singing. Toby then climbs out of the sewer (remember he promised Mrs. Lovett that nothing would harm her) grabs Sweeney's razor and from behind slits Todd's throat : 0 *gasp*