  Given a real function $f$ on an interval $[a,b]$ satisfying mild regularity
conditions, we determine the number of zeros of $f$ by evaluating a certain
integral. The integrand depends on $f, f'$ and $f''$. In particular, by
approximating the integral with the trapezoidal rule on a fine enough grid, we
can compute the number of zeros of $f$ by evaluating finitely many values of
$f,f'$ and $f''$. A variant of the integral even allows to determine the number
of the zeros broken down by their multiplicity.
