  A useful result is that if a bounded complex-valued path is
Riemann-integrable, then its modulus is also Riemann-integrable. The extension
of this last result to bounded paths taking values in a normed space is
affirmed, as being true, in [3]. However, we show that if a bounded path taking
values in a normed space is barely Riemann-integrable, then it is not really
guaranteed that the norm of this path is also Riemann-integrable.
