So, as we have been taught, the difference between Definite and Indefinite Integration is that Definite integration has limits and Indefinite Integration doesn't have limits. But, say the definite integral is, $$\int_{-\infty}^{+\infty} f(x) dx$$ why would it be any different than just integrating it normally as,
$$\int f(x) dx$$
If the bounds themselves in a definite integral are infinite what makes it any different to an indefinite integral.