  We consider the numerical computation of finite-range singular integrals
  $$I[f]=\intBar^b_a f(x)\,dx,\quad f(x)=\frac{g(x)}{(x-t)^m},\quad
m=1,2,\ldots,\quad
  a<t<b,$$ that are defined in the sense of Hadamard Finite Part, assuming that
$g\in C^\infty[a,b]$ and $f(x)\in C^\infty(\mathbb{R}_t)$ is $T$-periodic with
  $\mathbb{R}_t=\mathbb{R}\setminus\{t+ kT\}^\infty_{k=-\infty}$,
  $T=b-a$. Using a generalization of the Euler--Maclaurin expansion developed
in [A. Sidi,
  {Euler--Maclaurin} expansions for integrals with arbitrary algebraic endpoint
singularities. {\em Math. Comp.}, 81:2159--2173, 2012], we unify the treatment
of these integrals. For each $m$, we develop a number of numerical quadrature
formulas $\widehat{T}^{(s)}_{m,n}[f]$ of trapezoidal type for $I[f]$. For
example, three numerical quadrature formulas of trapezoidal type result from
this approach for the case $m=3$, and these are
  \begin{align*}
\widehat{T}^{(0)}_{3,n}[f]&=h\sum^{n-1}_{j=1}f(t+jh)-\frac{\pi^2}{3}\,g'(t)\,h^{-1}
  +\frac{1}{6}\,g'''(t)\,h, \quad h=\frac{T}{n},
  \widehat{T}^{(1)}_{3,n}[f]&=h\sum^n_{j=1}f(t+jh-h/2)-\pi^2\,g'(t)\,h^{-1},\quad
h=\frac{T}{n},
  \widehat{T}^{(2)}_{3,n}[f]&=2h\sum^n_{j=1}f(t+jh-h/2)-
\frac{h}{2}\sum^{2n}_{j=1}f(t+jh/2-h/4),\quad h=\frac{T}{n}.\end{align*}
