What does a student gain if he gets all the knowledge/skills in the world but loses his soul (Mark 8:36)? Eternal life is knowing the one true God and Jesus his Son (John 17:3). The heavens declare his glory (Psalm 19) and all things hold together in Him (Colossians 1:15-20). This means that every subject holds together in Him, and is custom-made for his praise.
John 1:3 says, “Through him all things were made; without him nothing was made that has been made.” Therefore, it would be idolatrous for us to teach a part of his world without reference to his design, his rule, or his presence. Science is his. Math is his. Grammar is his. History, philosophy, and the like. His Word tells us about the Fall, which has led to every brokenness in every subject. The results of sin must also be recognized, and this is a part of biblical integration.
Basically, the goal of biblical integration should be to see things as they are. Seeing, really seeing, will lead to worship and shape worldview.
For more on the basics look at the What is Biblical Integration? page.