  When a real-valued function of one variable is approximated by its $n^{th}$
degree Taylor polynomial, the remainder is estimated using the Alexiewicz and
Lebesgue $p$-norms in cases where $f^{(n)}$ or $f^{(n+1)}$ are
Henstock--Kurzweil integrable. When the only assumption is that $f^{(n)}$ is
Henstock--Kurzweil integrable then a modified form of the $n^{th}$ degree
Taylor polynomial is used. When the only assumption is that $f^{(n)}\in C^0$
then the remainder is estimated by applying the Alexiewicz norm to Schwartz
distributions of order 1.
