  Thermodynamic speed limits are a set of classical uncertainty relations that,
so far, place global bounds on the stochastic dissipation of energy as heat and
the production of entropy. Here, instead of constraints on these thermodynamic
costs, we derive integral speed limits that are upper and lower bounds on a
thermodynamic benefit -- the minimum time for an amount of mechanical work to
be done on or by a system. In the short time limit, we show how this extrinsic
timescale relates to an intrinsic timescale for work, recovering the intrinsic
timescales in differential speed limits from these integral speed limits and
turning the first law of stochastic thermodynamics into a first law of speeds.
As physical examples, we consider the work done by a flashing Brownian ratchet
and the work done on a particle in a potential well subject to external
driving.
