  If $f$ is a Henstock--Kurzweil integrable function on the real line, the
Alexiewicz norm of $f$ is $\|f\|=\sup_I|\int_I f|$ where the supremum is taken
over all intervals $I\subset\R$. Define the translation $\tau_x$ by
$\tau_xf(y)=f(y-x)$. Then $\|\tau_xf-f\|$ tends to 0 as $x$ tends to 0, i.e.,
$f$ is continuous in the Alexiewicz norm. For particular functions,
$\|\tau_xf-f\|$ can tend to 0 arbitrarily slowly. In general,
$\|\tau_xf-f\|\geq {\rm osc}f |x|$ as $x\to 0$, where ${\rm osc}f$ is the
oscillation of $f$. It is shown that if $F$ is a primitive of $f$ then
$\|\tau_xF-F\|\leq \|f\||x|$. An example shows that the function $y\mapsto
\tau_xF(y)-F(y)$ need not be in $L^1$. However, if $f\in L^1$ then
$\|\tau_xF-F\|_1\leq \|f\|_1|x|$. For a positive weight function $w$ on the
real line, necessary and sufficient conditions on $w$ are given so that
$\|(\tau_xf-f)w\|\to 0$ as $x\to 0$ whenever $fw$ is Henstock--Kurzweil
integrable. Applications are made to the Poisson integral on the disc and
half-plane. All of the results also hold with the distributional Denjoy
integral, which arises from the completion of the space of Henstock--Kurzweil
integrable functions as a subspace of Schwartz distributions.
