  The high-energy non-thermal universe is dominated by power law-like spectra.
Therefore results in high-energy astronomy are often reported as parameters of
power law fits, or, in the case of a non-detection, as an upper limit assuming
the underlying unseen spectrum behaves as a power law. In this paper I
demonstrate a simple and powerful one-to-one relation of the integral upper
limit in the two dimensional power law parameter space into the spectrum
parameter space and use this method to unravel the so far convoluted question
of the sensitivity of astroparticle telescopes.
