Find the area bounded by `y = x^(3)` and `x` -axis between ordinates `x = - 1` and `x = 1`.

Explanation

To find the area bounded by the curve \( y = x^3 \) and the x-axis between the ordinates \( x = -1 \) and \( x = 1 \), we will follow these steps:

### Step 1: Understand the Problem
We need to find the area between the curve \( y = x^3 \) and the x-axis from \( x = -1 \) to \( x = 1 \). The curve \( y = x^3 \) is symmetric about the origin and crosses the x-axis at \( x = 0 \).

### Step 2: Set Up the Integral
Since the area under the curve from \( x = -1 \) to \( x = 0 \) is below the x-axis, we will take the negative of the integral for that part. The area from \( x = 0 \) to \( x = 1 \) will be taken as is. Therefore, the total area \( A \) can be expressed as:
\[
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