The integral $\int_{0}^{1}\left(5 x^{3}+4 x^{2}+3 x+2\right) \mathrm{d} x$ is estimated numerically using three alternative methods namely the rectangular, trapezoidal and Simpson's rules with a common step size. In this context, which one of the following statements is TRUE?
(A) Simpson's rule as well as rectangular rule of estimation will give NON-zero error.
(B) Simpson's rule, rectangular rule as well as trapezoidal rule of estimation will give NON-zero error.
(C) Only the rectangular rule of estimation will give zero error.
(D) Only Simpson's rule of estimation will give zero error.
The integral $\int_{0}^{1}\left(5 x^{3}+4 x^{2}+3 x+2\right) \mathrm{d} x$ is estimated numerically using three alternative methods namely the rectangular, trapezoidal and Simpson's rules with a common step size. In this context, which one of the following statements is TRUE?
(A) Simpson's rule as well as rectangular rule of estimation will give NON-zero error.
(B) Simpson's rule, rectangular rule as well as trapezoidal rule of estimation will give NON-zero error.
(C) Only the rectangular rule of estimation will give zero error.
(D) Only Simpson's rule of estimation will give zero error.
Only Simpson's rule of estimation will give zero error.