Anti derivative notation [duplicate]

$F$ is an anti derivative of $f$.

$$\int f(x) dx = F(x)+C$$

Can you tell me why there is '$dx$' in the LHS?

• $\int f(x)$ wouldn't make sense. – user14972 Jul 12 '14 at 23:38

Take the differential of both sides: $dF=fdx$. Now, if the notation behaved like a regular fraction, we would have $dF/dx=f$, which means $f$ is the derivative of $F$ with respect to $x$. You may also consider the integral as a sum of $f(x)$ when $x$ varies as much as $dx$, which is an infinitesimal amount.