The integral you provided is:

\[
\int_0^1 1 \, dx
\]

This represents the area under the constant function $ f(x) = 1 $ between $ x = 0 $ and $ x = 1 $.

### Solution:

\[
\int_0^1 1 \, dx = [x]_0^1 = 1 - 0 = 1
\]

Thus, the value of the integral is $ \boxed{1} $.

Would you like further details or clarification? 

Here are some related questions:

1. How would you calculate the integral of a constant function over different intervals?
2. What is the general rule for integrating constant functions?
3. How does the area under a curve relate to integrals?
4. What happens if the constant function is negative, say $ f(x) = -1 $?
5. How do you approach integrals of piecewise constant functions?

**Tip:** The integral of a constant function $ f(x) = c $ over an interval $ [a, b] $ is simply $ c(b - a) $.

The integral you provided is: $$ \int_0^1 1 \, dx $$

Learn how to evaluate the integral of a constant function, $ f(x) = 1 $, over the interval [0, 1]. This problem covers key concepts in integral calculus, including the area under a constant curve. Suitable for students in Grades 9-12.

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