An automated actuator exerts a variable force along the x-axis on an object, given by the function \(F(x) = bx^2 + c\), where \(b = 3.0 \text{ N/m}^2\) and \(c = 4.0 \text{ N}\). What is the work done by this force on the object as it moves from \(x = 1.0 \text{ m}\) to \(x = 2.0 \text{ m}\)?