Find the formula for the function represented by the integral.
(Use symbolic notation and fractions where needed.)
\[
\int_{0}^{x} \sin (6 u) d u=
\]

Step 1 ：The integral of a function can be found by finding the antiderivative of the function. In this case, the function is \( \sin(6u) \).

Step 2 ：The antiderivative of \( \sin(6u) \) is \( -\frac{1}{6} \cos(6u) \).

Step 3 ：However, we are given a definite integral from 0 to x. So, we need to evaluate the antiderivative at x and at 0, and subtract the two.

Step 4 ：Evaluating the antiderivative at x gives \( -\frac{\cos(6x)}{6} \).

Step 5 ：Evaluating the antiderivative at 0 gives \( -\frac{1}{6} \).

Step 6 ：Subtracting these two values gives the definite integral \( \frac{1}{6} - \frac{\cos(6x)}{6} \).

Step 7 ：Final Answer: The formula for the function represented by the integral is \( \boxed{\frac{1}{6} - \frac{\cos(6x)}{6}} \).