Integrated cross sections for 1s-1s, 1s-2s and 1s-2p electron-hydrogen-atom scattering processes are reported for scattering energies ranging from the ionisation threshold to 4 Ryd. For the total angular momentum L in the range 0<or=L<or=4 the intermediate energy R-matrix theory of Burke et al. (1981) has been used. From L=5 to L=Lmax, where Lmax varies between 10 and 16, calculations have been performed using the standard R-matrix close-coupling method and employing the nine-state basis (three eigenstates plus six pseudostates) of Fon et al. (1981). To compensate for incompleteness in the R-matrix bases, corrections have been applied to all partial waves 0<or=L<or=Lmax using the plane-wave second Born approximation. In addition, the second Born approximation has also been used to extrapolate the partial-wave series from L=Lmax+1 to infinity. The agreement with theoretical work of Callaway et al. (1987) is good for both elastic and inelastic processes. The calculated 1s-2s and 1s-2p cross sections are in reasonable accord with experimental results originating from the 1s-2p relative data of Long et al. (1968) independently normalised to theory at high energy and with the 2s/2p ratio measurements of Kauppila et al. (1970). However at 4 Ryd the 1s-2p result lies below an absolute measurement of Williams (1981) and confirms an earlier theoretical result of van Wyngaarden and Walters (1986). Finally the total inelastic cross section is reported.