I have a task where I need to calculate $\displaystyle \int_{0}^{1} \sinh(x) \,dx$. I know that to integrate $\displaystyle \int_{0}^{\pi/2} \sin(x) \,dx$ we take $\Delta x_i = \dfrac{\pi }{ 2n}$ and $x_i = \dfrac{i\pi }{2n}$, so
$\displaystyle \epsilon_n = \sum_{i=1}^{n} \sin\left(\frac{i\pi}{2n}\right) \times \frac{\pi}{2n}$ where we can use that $\dfrac {\sin(x)}{x}$ is very close to 1 when $x$ is close to 0 to simplify.
But what to do here? Thanks in advance.