If f is a Henstock-Kurzweil integrable function on the real line, the Alexiewicz norm of f is || f || = sup I | f I f| where the supremum is taken over all intervals I ⊂ . Define the translation τx by τxf(y) = f(y − x). Then ||τxf − f || tends to 0 as x tends to 0, i.e., f is continuous in the Alexiewicz norm. For particular functions, ||τxf − f || can tend to 0 arbitrarily slowly. In general, ||τxf − f || ≥ osc f|x| as x → 0, where osc f is the oscillation of f. It is shown that if F is a primitive of f then ||τxF − F || || ≤ ||f || |x|. An example shows that the function y → τxF(y) − F(y) need not be in L 1 . However, if f ∈ L 1 then || τxF − Fk1 || ≤ || f ||1|x|. For a positive weight function w on the real line, necessary and sufficient conditions on w are given so that ||(τxf − f)w || → 0 as x → 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.