[en] We have measured the spin structure functions g₁ and g₂ of ³He in a double-spin experiment by inclusively scattering polarized electrons at energies ranging from 0.862 to 5.07 GeV off a polarized ³He target at a 15.5^o scattering angle. Excitation energies covered the resonance and the onset of the deep inelastic regions. We have determined for the first time the Q² evolution of Γ₁(Q²)=/int₀¹ g₁(x,Q²) dx, Γ₂(Q²)=/int₀¹ g₂(x,Q²) dx and d₂ (Q²) = /int₀¹ x ²[2g₁(x,Q²) + 3g₂(x,Q²)] dx for the neutron in the range 0.1 GeV² /leq Q² /leq 0.9 GeV² with good precision. Γ₁(Q²) displays a smooth variation from high to low Q². The Burkhardt-Cottingham sum rule holds within uncertainties and d₂ is non-zero over the measured range