1.0 Theoretical Meaning

Let $f$ be the continuous function in $\left[ {a,b} \right]$ and $F$ be an anti-derivative of $f$, then definite integral of $f\left( x \right)$ is defined as

$$\int\limits_a^b {f\left( x \right)dx} $$ $$ = \left[ {F\left( x \right)} \right]_a^b$$ $$ = F\left( b \right) - F\left( a \right)$$

where $a$ is lower limit of the integral and $b$ is upper limit of the integral.

Value of any definite integral is unique.