  We present for the first time a determination of the energy dependence of the
isoscalar $\pi\pi$ elastic scattering phase-shift within a first-principles
numerical lattice approach to QCD. Hadronic correlation functions are computed
including all required quark propagation diagrams, and from these the discrete
spectrum of states in the finite volume defined by the lattice boundary is
extracted. From the volume dependence of the spectrum we obtain the $S$-wave
phase-shift up to the $K\overline{K}$ threshold. Calculations are performed at
two values of the $u,d$ quark mass corresponding to $m_\pi = 236, 391$ MeV and
the resulting amplitudes are described in terms of a $\sigma$ meson which
evolves from a bound-state below $\pi\pi$ threshold at the heavier quark mass,
to a broad resonance at the lighter quark mass.
