You’ve provided an integral equation:

$\int_{0}^{1} f(x) \, dx = 1$

This means the definite integral of $f(x)$ from 0 to 1 equals 1. In simpler terms, the area under the curve $f(x)$ from $x = 0$ to $x = 1$ is equal to 1.

Would you like to:

1. Solve for $f(x)$ if additional conditions are given?
2. Explore examples of functions $f(x)$ that satisfy this condition?
3. Learn about the properties of definite integrals?
4. Find the average value of $f(x)$ over $[0, 1]$?
5. Analyze a scenario where $f(x)$ is a probability density function?

Tip: If $f(x)$ is a probability density function, this condition means the total probability is normalized to 1 over the interval $[0, 1]$.