# Riemann Sum of Ratio of Equation of Lines

Question: Can all kinds of summation be transformed into a Riemann Sum so that it can be transformed into a definite integral?

Consider this limit: \begin{align} L=\lim\limits_{n\to\infty}\sum_{i=1}^n\dfrac{m\left[a+i\dfrac{b-a}{n}\right]+c}{m\left[a+(i-1)\dfrac{b-a}{n}\right]+c}, \end{align}

where $a, b, c, m$ are non-zero and $b>a$. I searched other answers and some are using squeeze theorem, which I don't know how to apply to this problem. Can someone show me step-by-step procedure on how to transform this sum into definite integral?