What is the derivative with respect to x of the function F(x) = ∫[0 to x²] sin t dt?

What is the derivative with respect to x of the function F(x) = ∫[0 to x²] sin t dt?

• A. sin(x²)
• B. 2x sin(x²)
• C. cos(x²)
• D. -2x cos(x²)

Answer: B) 2x sin(x²)

Explanation: Using the Leibniz rule (Chain Rule with FTC): d/dx [ ∫[a to g(x)] f(t) dt ] = f(g(x)) × g'(x). Here, g(x) = x², so the derivative is sin(x²) × 2x.