Final answer:
The question is about estimating the integral of a function using Simpson's Rule in mathematics, typically a high school calculus topic. However, without the function values at specific points, we cannot apply Simpson's Rule to estimate the integral.
Step-by-step explanation:
The subject of this question is Mathematics, specifically numerical integration using Simpson's Rule. The grade level most appropriate for this question is High School, as this concept typically appears in calculus courses, which are often a part of a high school math curriculum. To use Simpson's Rule, we need an even number of intervals and the values of the function at equidistant points within the range of integration. Simpson's Rule is given by:
S = (Δx/3) [y0 + 4(y1 + y3 + ... + yn-1) + 2(y2 + y4 + ... + yn-2) + yn]
Where Δx is the width of each interval, n is the number of intervals that must be even, y0...yn is the function values at the start, end, and intermediate points of the intervals. However, to accurately answer the question with the provided table, we would need the specific y values at x = 6, 7, 8, 9, 10, 11, and 12 to apply Simpson's Rule. Without this information, we cannot estimate the integral using Simpson's Rule.