Let `f` be a real-valued function satisfying `f(x)+f(x+4)=f(x+2)+f(x+6)` Prove that `int_x^(x+8)f(t)dt` is constant function.

Explanation

To prove that the integral \( \int_x^{x+8} f(t) \, dt \) is a constant function, we start with the functional equation given:

\[ f(x) + f(x+4) = f(x+2) + f(x+6) \]

### Step 1: Substitute \( x \) with \( x + 2 \)

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