So in attempting to prove the pointwise convergent result $$\lim_{N\to\infty} S_N(f)(x) = f(x)$$ provided $$\exists \space \delta>0 \space \text{s.t.} \space |f(x+t) - f(x)| \leq C|t| \text{ for } |t| < \delta.$$
I'm seeing the following step taking place:
$$ \begin{multline}\left|\frac{1}{2\pi} \int_{-\pi}^{\pi} f(x) D_n(x-y)\, dy - f(x)\right|\\ = \left|\frac{1}{2\pi} \int_{-\pi}^{\pi} f(x) D_n(x-y) \,dy - f(x) \dfrac{1}{2\pi} \int_{-\pi}^{\pi} D_N(y)\,dy\right|. \end{multline}$$
Is $\frac{1}{2\pi} \int_{-\pi}^{\pi} D_N(y)\,dy = 1$, or how was this term added in?