  We perform a cosmic shear analysis of HSC survey first-year data (HSC-Y1)
using Complete Orthogonal Sets of E/B-Integrals (COSEBIs) to derive
cosmological constraints. We compute E/B-mode COSEBIs from cosmic shear
two-point correlation functions measured on an angular range of
$4\arcmin<\theta<180\arcmin$. We perform the standard Bayesian likelihood
analysis for cosmological inference from the measured E-mode COSEBIs, including
contributions from intrinsic alignments of galaxies as well as systematic
effects from point spread function model errors, shear calibration
uncertainties, and source redshift distribution errors. We adopt a covariance
matrix derived from realistic mock catalogs constructed from full-sky
gravitational lensing simulations that fully take account of the survey
geometry and measurement noise. For a flat $\Lambda$ cold dark matter model, we
find $S_8 \equiv \sigma_8\sqrt{\Omega_m/0.3}=0.809_{-0.026}^{+0.036}$. We
carefully check the robustness of the cosmological results against
astrophysical modeling uncertainties and systematic uncertainties in
measurements, and find that none of them has a significant impact on the
cosmological constraints. We also find that the measured B-mode COSEBIs are
consistent with zero. We examine, using mock HSC-Y1 data, the consistency of
our $S_8$ constraints with those derived from the other cosmic shear two-point
statistics, the power spectrum analysis by Hikage et al (2019) and the
two-point correlation function analysis by Hamana et al (2020), which adopt the
same HSC-Y1 shape catalog, and find that all the $S_8$ constraints are
consistent with each other, although expected correlations between derived
$S_8$ constraints are weak.

Cosmology and Nongalactic Astrophysics