calculus - Find the limit : $limlimits_{nrightarrowinfty}int_{n}^{n+7}frac{sin{x}}{x},mathrm dx$

I have this exercise I don't know how to approach :

Find the limit : $$\lim_{n\rightarrow\infty}\int_{n}^{n+7}\frac{\sin x}{x}\,\mathrm dx$$

I can see that with $n\rightarrow\infty$ the area under the graph of this function becomes really small as $\sin{x} \leq 1$ so $\dfrac{\sin{n}}{n}\rightarrow_{\infty}0$ but can I get something from it?

Answer

Hint: $\def\abs#1{\left|#1\right|}$
$$\abs{\int_n^{n+7}\frac{\sin x} x \, dx}\le \int_n^{n+7}\frac{\abs{\sin x}}{x}\, dx\le \frac 1n \int_n^{n+7}\abs{\sin x}\, dx $$