Determining $a$ and $b$ when $\int_a^b\sin x\,dx$ is given as a Riemann sum

Question

Determine $a$ and $b$ such that $$\lim_{n\to\infty}\sum_{i=0}^n\sin\left(\left(2+\frac{3}{2n}\right)+\frac{3}{n}i\right)\cdot\frac{3}{n} = \int_a^b\sin x\;dx$$

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$a$ should equal $2$, and $b$ should equal $5$. I don't understand how. If $\Delta x = 3/n$, shouldn't it be $f\left(a+\frac{3i}{n}\right)$? Where is the $\frac{3}{2n}$ coming from?

Can someone please help me with this?