So I came across with this integral today in my midterm:
$$ \int \frac {\tan(\pi x)\sec^2(\pi x)}2 $$
And I got two correct answers:
$$\frac {\sec^2(\pi x)}{4\pi} +C$$
And
$$\frac {\tan^2(\pi x)}{4\pi} + C$$
The first one, I get it by substituting $u=\sec (\pi x)$ and the second one, by substituting $u=\tan (\pi x) $
I already differentiated both answers and got to the same integral, but my question is, if both answers are correct and if it were a definite integral, which answer should I use? Wouldn't they give different results?