  We solve two stochastic control problems in which a player tries to minimize
or maximize the exit time from an interval of a Brownian particle, by
controlling its drift. The player can change from one drift to another but is
subject to a switching cost. In each problem, the value function is written as
the solution of a free boundary problem involving second order ordinary
differential equations, in which the unknown boundaries are found by applying
the principle of smooth fit. For both problems, we compute the value function,
we exhibit the optimal strategy and we prove its generic uniqueness.
