Apply the Trapezoidal Rule and Simpson's Rule to Approximate the Value

Multiple Choice

Apply the Trapezoidal Rule and Simpson's Rule to approximate the value of the definite integral using 8 subintervals. Round your answer to six decimal places and compare the result with the exact value of the definite integral.
$\int _ { 4 } ^ { 5 } \sqrt { 4 + t ^ { 5 } } d t$

A) The Trapezoidal rule gives $43.377044$ and Simpson's rule gives $45.513198$ .
B) The Trapezoidal rule gives $43.345903$ and Simpson's rule gives $43.335523$ .
C) The Trapezoidal rule gives 43.377044 and Simpson's rule gives 43.335523.
D) The Trapezoidal rule gives $43.345903$ and Simpson's rule gives $45.513198$ .
E) The Trapezoidal rule gives $- 43.345903$ and Simpson's rule gives $- 43.335523$ .