simple question on Born

If I have the formulation right, the Born rule says that the probability that a measurement for the position of the particle at time t will be in the real interval [a,b] equals ∫_a^b|ψ(x,t)|²dx. Fine. So, is the probability that a continuous measurement for the position of the particle will be in the real interval [a,b] at least once during the time interval [t1,t2] just equal to ∫_t1^t2∫_a^b|ψ(x,t)|²dx dt, or does this not work? If not, is there a more appropriate calculation?