1. The problem states that \(F(x) = \int_{-2}^x f(t) \, dt\) where \(f\) is continuous on \([-2,2]\). 2. By the Fundamental Theorem of Calculus, if \(F(x) = \int_a^x f(t) \, dt\) and \(f\) is continuous, then \(F'(x) = f(x)\). 3. Since \(F(x)\) is defined as \(\int_{-2}^x f(t) \, dt\), the derivative \(F'(x)\) is simply \(f(x)\) for all \(x \in [-2,2]\). 4. Therefore, the expression for the derivative of \(F\) on \([-2,2]\) is: $$F'(x) = f(x)$$ This derivative exists everywhere on the interval because \(f\) is continuous there.