We believe in the Old Testament because Christ Jesus affirmed the Old Testament.  Throughout Christ ministry He affirmed the scripture of His day and the apostles also referred to it. However this scripture is the Septuagint bible NOT the Masoretic OT.  The Septuagint bible is older that the Masoretic OT. The Septuagint is the first translation from OLD Hebrew to Greek done in around 200-300 BC because James the Great had conquered the land and the common language of the people of that time, including Jews, was not Old Hebrew BUT Koine Greek and Aramaic. The Masoretic OT is a translation done around 300AD from Old Hebrew to the Current Hebrew and it was done hundreds of years after the crucifixion of our Lord Jesus Christ. This may explain why the Masoretic OT leaves out many verses about Christ!
Early Christian believers and churches (including the Catholic Church) used the Septuagint bible BUT it was a Catholic priest during the 4th century that under many protestors decided to use the Masoretic OT to translate to Latin and create the first Latin bible known as the Vulgate. 
The Dead Sea Scrolls includes the Septuagint writing.

We believe in the 27 books of the New Testament because the Lord Jesus Christ authorized His apostles to write the New Testament." (See John 14-16, John 16:12-15, Matthew 28:18-19, Acts 1:8, 2Peter3:19-21 "Every book of the NT was written under apostolic authority-either by an apostle or someone linked to apostolic ministry."
The reason the canon is closed is because there are no longer any apostles in the church today and have not been any since the end of the first century, with the conclusion of the foundation age of the church (Eph 2:20). Therefore any writings after this time including the religions that were created after this time is NOT from GOD!
(For more information refer to The Bible Tab!)