Its a tenant of faith in Islam, to believe in Jesus (upon him peace) and the Bible. How we believe in them is that Jesus is a Prophet like other Prophets. The bible was unfortunately corrupted over time due to many factors as many Christan scholars confirm.
The Quran does not say that to be a good Muslim, you have to follow the bible, in fact Muslims have the Quran and do not need another book.
So its part of faith to believe in the books of God, Torah, Gospel, Psalms of David and finally the Quran. And the Quran is only book that is valid because this remains in the language of its Revelation 1400 or so, years later.