Numerical Analysis — degree of precision of quadrature rules

Consider the following statements: I. Trapezoidal rule for evaluating $\int_a^b f(x)\,dx$ gives exact result for linear polynomial. II. Trapezoidal rule for evaluating $\int_a^b f(x)\,dx$ gives exact result for quadratic polynomial. III. Simpson's one-third rule for evaluating $\int_a^b f(x)\,dx$ gives exact result for cubic polynomial. IV. Simpson's one-third rule for evaluating $\int_a^b f(x)\,dx$ gives exact result for quadratic polynomial. Which of the statements given above are correct?