  We consider estimating the magnitude of a monochromatic AC signal that
couples to a two-level sensor. For any detection protocol, the precision
achieved depends on the signal's frequency and can be quantified by the quantum
Fisher information. To study limitations in broadband sensing, we introduce the
integrated quantum Fisher information and derive inequality bounds that embody
fundamental tradeoffs in any sensing protocol. These inequalities show that
sensitivity in one frequency range must come at a cost of reduced sensitivity
elsewhere. For many protocols, including those with small phase accumulation
and those consisting of $\pi$-pulses, we find the integrated Fisher information
scales linearly with $T$. We also find protocols with substantial phase
accumulation can have integrated QFI that grows quadratically with $T$, which
is optimal. These protocols may allow the very rapid detection of a signal with
unknown frequency over a very wide bandwidth.
