  For a Banach space $X$ we demonstrate the equivalence of the following two
properties:
  (1) $X$ is B-convex (that is, possesses a nontrivial infratype), and
  (2) if ${F: [0,1] \to 2^{X} \setminus \{\varnothing\}}$ is a {multifunction},
$\mathrm{conv} F$ denotes the mapping $t \mapsto \mathrm{conv} F(t)$, then the
Riemann integrability of $\mathrm{conv} F$ is equivalent to the Riemann
integrability of $F$.
  For multifunctions with compact values the Riemann integrability of
$\mathrm{conv} F$ is equivalent to the Riemann integrability of $F$ without any
restrictions on the Banach space $X$.
