A block of mass \(m\) is initially at rest at position \(x = 0\) on a frictionless horizontal surface. Starting at time \(t = 0\), a net horizontal force with magnitude \(F(x) = \beta x^2\) is applied to the block in the \(+x\)-direction, where \(\beta\) is a positive constant. Which of the following integrals correctly represents the magnitude of the impulse delivered to the block as it travels from \(x = 0\) to \(x = L\)?