Words spoken by Jesus about the old testament:
John 10:35
"Scripture cannot be set aside"
Matthew 5:18
"For truly i say unto you, until heaven and earth pass away, not the smallest letter or stroke shall pass away from the law, until all is accomplished"
Matthew 22:31
"Have you not read what was said to you by God"
We can deduce that in terms of authority Jesus affirms the old testament.
But what about the historicity? Did Jesus believe all the events of the old testament actually happened?
Let's see what he says:
Luke 17:29
"On the day when Lot went out of Sodom, fire and sulfur rained down from heaven and destroyed them all"
Luke 11:51
"From the blood of Abel to the blood of Zechariah, who perished between the altar and the sanctuary"
Matthew 19:4
"Haven't you read that at the beginning the Creator made them male and female?"
So, is Jesus lying? Is he ignorant of science and history? Or is the old testament including genesis literally true, and the world is ~6000 years old as per the lifespans of the full genealogy from the beginning of the world given in matthew 1?
Mark 12:26
"Have you not read in the book of Moses, in the passage about the bush, how God spoke to him, saying, 'I am the God of Abraham, and the God of Isaac, and the God of Jacob'?"
John 6:31
"Our fathers ate manna in the wilderness"