অনির্দিষ্ট যোগজ কোনো সংখ্যা নয়

This is a common misconception about integration. An indefinite integral yields a function. That is,

$$\int{f'(x)dx} = f(x) + C$$

The result will be a function in terms of $x$ (with the one exception being $f'(x) = 0$).

However, a definite integral is the indefinite integral defined on a certain timespan, so as long as $f'(x)$ has an antiderivative:

$$\int^{b}_{a}{f'(x)dx} = K$$

$K$ is a real number. According to the Fundamental Theorem of Calculus, $K$ is found by $f(b) - f(a)$.

In summary, we only get a number with definite integration, and we get a function at no specific value of $x$ with indefinite integration.