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We have calculated the inverse Compton (IC) integrated spectral power within the Thomson limit for a monoenergetic isotropic photon field upscattered off highly relativistic electrons assuming an isotropic powerlaw distribution of the latter, N (γ ) = Cγ −p, with Lorentz parameter values γ1 < γ < γ2. Our interest was essentially focused on the case of a finite energy range (finite γ2) possibly having realistic applications in highenergy astrophysical sites, mainly relativistic shock regions. To this end, we have defined and derived a dimensionless parametric function, Fp(z1, η), with variables z1 = 1/4γ 2 1 and η = γ2/γ1. This result was used to derive the IC-integrated spectral power for an upscattered blackbody (BB) photon field using a dimensionless parametric function, Wp(ξ, η), with variable ξ = 1/4γ 2 1 kT . Asymptotic forms of this function have been derived for three energy ranges, i.e., ξ 1, 1 ξ η2, and ξ η2. Then, a characteristic value, ηc(p, ε) with ε 1, of parameter η was defined such that the middle range asymptotic form of Wp(ξ, η) could be valid and good when η ηc(p, ε), by deriving an approximate expression of this particular value for ε = 10−3. The resulting spectra featured by a high-energy cutoff in the case of low values of the ratio η can be discussed at least for a population of short gamma-ray bursts (GRBs), those best described by the cutoff power-law model with a low-energy spectral index, α ≈ 0. Furthermore, it is suggested that for GRB spectra with α < −1/2 pertaining to the prompt emission phase, the IC is a likely emission mechanism for both monoenergetic and BB photon fields if one assumes that the former photon field could exist specifically in the GRB environment. Various suitable astrophysical applications are presented and discussed.