Riemann Integration

Interval

Let $I=[a,b]$. Length of the interval $\lvert{I}\rvert=b-a$.

Disjoint interval

When 2 intervals don’t share any common numbers.

Almost disjoint interval

When 2 intervals are disjoint or intersect only at a common endpoint.

Riemann Integral

Let $f\,-\,[a,b]\rightarrow\mathbb{R}$ is a bounded function on a closed, bounded (compact) interval. $$

Riemann integral of $f$ is: $$

$$\int_{a}^{b}{f}$$

Definite integral

When $a,b$ are constants. $$

Indefinite integral

When $a$ is a constant but $b$ is replaced with $x$.