By using the properties of definite integrals, evaluate the integrals `int_(-pi/2)^(pi/2)sin^7x dx`

Explanation

To evaluate the integral \( I = \int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} \sin^7 x \, dx \) using the properties of definite integrals, we can follow these steps:

### Step 1: Identify the function
The integrand is \( f(x) = \sin^7 x \).

### Step 2: Check if the function is odd or even
To determine whether the function is odd or even, we need to evaluate \( f(-x) \):
\[
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