Let $\psi : \mathbb{R} \rightarrow \mathbb{R}$ be a continuous function with $\int_{-1}^{1} \psi(x)\,\mathrm{d}x = 1$. Let $f : \mathbb{R} \rightarrow \mathbb{R}$ be a differentiable function. Then
$$\lim_{\varepsilon \rightarrow 0} \frac{1}{\varepsilon} \int_{1-\varepsilon}^{1+\varepsilon} f(y)\,\psi\!\left(\frac{1-y}{\varepsilon}\right) \mathrm{d}y$$
equals\\
(A) $f(1)$\\
(B) $f(1)\psi(0)$\\
(C) $f'(1)\psi(0)$\\
(D) $f(1)\psi(1)$