Application Of Integrals

Note: The provided question with yields an answer of , which is not among the options. It is highly likely that the question intended to ask for , as handwritten '3' and '5' can look similar, and the correct answer for is one of the options. We will proceed with this assumption.

Step 1: Understanding the Concept:

We need to find the area bounded by a curve and the x-axis. Since area is always a non-negative quantity, we must integrate the absolute value of the function, . The function is negative for and positive for .

Step 2: Key Formula or Approach:

The area is given by the definite integral of from -1 to 1: We must split the integral at where the function's sign changes.

Step 3: Detailed Explanation:

Let's split the integral into two parts:

For , is negative, so .
For , is positive, so .
Now, we integrate: Evaluate the first part: Evaluate the second part: The total area is the sum of the two parts:

Step 4: Final Answer:

Assuming the intended curve was , the area is square units.