$F$ is an anti derivative of $f$.
$$\int f(x) dx = F(x)+C$$
Can you tell me why there is '$dx$' in the LHS?
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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.