Consider the statements
S1: If \( f(a) \cdot f(b)<0 \) then there exists a root for \( f(x) = 0 \) in between \( a \) and \( b \)
S2: The Simpson's \( \frac{1}{3} \) rule approximates the definite integral
\[
\int_a^b f(x)\, dx
\]
as sum of the areas under the parabolas.
Which of the following is correct?