TITLE: $\int f(x)\,\mathrm{d}x = \left(\int_0^x f(t) \, \mathrm{d}t\right) + C$
QUESTION [14 upvotes]: If $f(x)$ is a continuous function on $\mathbb{R}$ and I am asked to find 
$\int f(x) \, dx$, what is the problem with the following answer:
$$\int f(x)\,\mathrm{d}x = \left(\int_0^x f(t) \, \mathrm{d}t\right) + C$$

REPLY [8 votes]: There are cases when it's appropriate do this:  
Someone says

$e^{-x^2}$ is not integrable  

So we say

Of course it is integrable.  All continuous functions are integrable.  The integral is $\int_0^x e^{-t^2}\;dt$.  What you mean is: the integral is not an elementary function.