প্রতিঅন্তরজকে মাঝেমধ্যে "অনির্দিষ্ট যোগজ"-ও বলা হয়

First thing you should know $-$ indefinite integrals and anti-derivatives are almost the same thing and are often interchanged in colloquial speech. Second thing you should know $-$ this is basically true!

The antiderivative of a function $f$ is a function whose derivative is $f$. An integral is either definite or indefinite. A definite integral is a number $-$ the result when bounds are inserted into the indefinite integral. An indefinite integral is simply an antiderivative, but we often say, for example, if $f(x)=x$:

An antiderivative of $f(x)=x$ is $F(x)=\frac{x^2}{2}$.

vs.

The indefinite integral of $f(x)=x$ is $F(x)=\frac{x^2}{2}+\mathcal{C}$, for an arbitrary constant $\mathcal{C}$.

As you can see, they are identical in concept, except the indefinite integral often times mentions the full family when an antiderivative does not have to.