1 Point
Suppose $f(t)$ is the temperature (in degrees Celsius) of a mysterious substance that you are studying in a lab after $t$ hours of observation. You measure the value of $f(t)$ in hourly intervals and record them in the following table:
$$\text{Unknown environment 'tabular'}$$
Determine the exact value of the definite integral
$${\int }_3^9{f}^{\prime }(t)dt$$
Please be aware that the function in the integral is $f^{\prime }$, which is the derivative of $f$. You may assume that $f$ is differentiable and $f^{\prime }$ is continuous for all values of $x$.

Step 1 ：The Fundamental Theorem of Calculus states that if a function $f$ is continuous on the interval $[a,b]$ and $F$ is an antiderivative of $f$ on the interval $[a,b]$, then ${\int }_a^{b}f(t)dt=F(b)-F(a)$

Step 2 ：In this case, we are asked to find the value of the definite integral ${\int }_3^9{f}^{\prime }(t)dt$

Step 3 ：Since $f^{\prime }(t)$ is the derivative of $f(t)$, we can say that $f(t)$ is an antiderivative of $f^{\prime }(t)$. Therefore, we can apply the Fundamental Theorem of Calculus to find the value of the integral: ${\int }_3^9{f}^{\prime }(t)dt=f(9)-f(3)$

Step 4 ：From the table, we know that $f(3)=14$ and $f(9)=17$. Substituting these values into the equation, we get ${\int }_3^9{f}^{\prime }(t)dt=17-14=3$

Step 5 ：So, the exact value of the definite integral is $\boxed{{\displaystyle 3}}$