  We consider stochastic integration with respect to fractional Brownian motion
(fBm) with $H < 1/2$. The integral is constructed as the limit, where it
exists, of a sequence of Riemann sums. A theorem by Gradinaru, Nourdin, Russo &
Vallois (2005) holds that a sequence of Simpson's rule Riemann sums converges
in probability for a sufficiently smooth integrand $f$ and when the stochastic
process is fBm with $H > 1/10$. For the case $H = 1/10$, we prove that the
sequence of sums converges in distribution. Consequently, we have an It\^o-like
formula for the resulting stochastic integral. The convergence in distribution
follows from a Malliavin calculus theorem that first appeared in Nourdin and
Nualart (2010).
