i’m very sorry but i have damaged your book for this reason....... i would like to give you some money on how much the book costs so i can replace it. i don’t think i can give the book back to you
Im very sorry for damaging your book. The incident that occurred was ..., and I wish I could fix it, So I will get you a new one tomorrow! Please trust me, and you will have a brand new book tomorrow
putting unbiased in the sentence would create a respectful response or opinion also stating that you do not have any favors to one side meaning it is a completely fair argument.