Riemann Sum to integral form

Question

Hi please help me in converting this Riemann Sum to integral form:

Any help would be greatly appreciated..!!

with $\Delta x={c\over an}$

Answer 1

Hint

The lim sum $\lim _{n\to\infty} \Delta x\sum_{k=1}^n f({k\over n})$ can be converted to $\int_0^1f(x)dx$ as long as $f(x)$ is integrable over $(0,1)$ and $\Delta x={1\over n}$, so first find $f(x)$ and then substitute $x={k\over n}$.

Update

In the question, it is mentioned that $\Delta x={c\over an}$, hence the integral must be something like $${c\over a}\int_0^1 f(x)dx$$