If $f(x)=\int_{x}^{13} t^{2} d t$ then
\[
f^{\prime}(x)=
\]

Step 1 ：Given the function \(f(x)=\int_{x}^{13} t^{2} dt\), we are asked to find its derivative \(f^{\prime}(x)\).

Step 2 ：We can use the Fundamental Theorem of Calculus Part 1 to solve this problem. According to the theorem, if a function \(f\) is continuous over the interval \([a, b]\) and \(F\) is an antiderivative of \(f\) on \([a, b]\), then \(\int_{a}^{b} f(x) dx = F(b) - F(a)\).

Step 3 ：In this case, the function inside the integral is \(t^2\), and the limits of the integral are \(x\) and \(13\). The derivative of the integral of a function is the original function itself.

Step 4 ：Therefore, the derivative of \(f(x)\) should be \(-x^2\).

Step 5 ：Final Answer: \(f^{\prime}(x) = \boxed{-x^2}\)