The definite integral of a function $f$ from $x=a$ to $x=b$ and $\Delta x = (b-a)/n$ is defined by the limit of a Riemann Sum:
$$ \int_{a}^{b} f(x) dx = \lim_{n \to \infty} \sum_{i=1}^{n} f(a+i\cdot\Delta x) \cdot \Delta x $$
I am curious about the definition of the indefinite integral expressed through the limit of a Riemann Sum. Could you also clarify the concepts of upper and lower bounds in this context?
$$ \int_{}^{} f(x) dx = \text{?} $$