Calculate the integral, assuming that ${\int }_0^{1}f(x)dx=2,{\int }_0^{2}f(x)dx=5,{\int }_1^{4}f(x)dx=12$. Determine if the integral calculation is correct. If not, identify the correct value using the ans
$${\int }_2^{4}f(x)dx=7$$

Step 1 ：Given that ${\int }_0^{1}f(x)dx=2$, ${\int }_0^{2}f(x)dx=5$, and ${\int }_1^{4}f(x)dx=12$

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, ${\int }_0^{4}f(x)dx={\int }_0^{1}f(x)dx+{\int }_1^{4}f(x)dx=2+12=14$

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, ${\int }_2^{4}f(x)dx={\int }_0^{4}f(x)dx-{\int }_0^{2}f(x)dx=14-5=9$

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