Calculate the integral, assuming that $\int_{0}^{1} f(x) d x=2, \int_{0}^{2} f(x) d x=5, \int_{1}^{4} f(x) d x=12$. Determine if the integral calculation is correct. If not, identify the correct value using the ans
\[
\int_{2}^{4} f(x) d x=7
\]

Step 1 ：Given that \(\int_{0}^{1} f(x) d x=2\), \(\int_{0}^{2} f(x) d x=5\), and \(\int_{1}^{4} f(x) d x=12\)

Step 2 ：We can calculate the integral of the function over the interval [0, 4] by adding the integral of the function over the interval [0, 1] to the integral of the function over the interval [1, 4]. So, \(\int_{0}^{4} f(x) d x = \int_{0}^{1} f(x) d x + \int_{1}^{4} f(x) d x = 2 + 12 = 14\)

Step 3 ：We can calculate the integral of the function over the interval [2, 4] by subtracting the integral of the function over the interval [0, 2] from the integral of the function over the interval [0, 4]. So, \(\int_{2}^{4} f(x) d x = \int_{0}^{4} f(x) d x - \int_{0}^{2} f(x) d x = 14 - 5 = 9\)

Step 4 ：Final Answer: The correct value of the integral from 2 to 4 is not 7, but \(\boxed{9}\)