Let's break down the image step by step.

The integral shown is: $1 \cdot \int u^2 \, du$

Step 1: Solve the integral

To solve this, we use the power rule of integration, which states: $\int u^n \, du = \frac{u^{n+1}}{n+1} + C$

Here, $n = 2$, so: $\int u^2 \, du = \frac{u^{3}}{3}$

Step 2: Apply the limits (although not shown, they must be 1 and 0)

To evaluate the integral from 1 to 0, we plug in the limits: $\left[ \frac{u^3}{3} \right]_1^0 = \frac{0^3}{3} - \frac{1^3}{3} = 0 - \frac{1}{3} = -\frac{1}{3}$

However, the final result shows $5$, indicating a possible miscalculation or assumption in the original problem setup. Based on the answer choices, none directly match the actual calculation unless some missing context is involved.

Can you confirm if there are specific limits, or is there additional context for this integral? Meanwhile, the given steps show the method used is not yielding those exact options. Let me know if you'd like to go further.

Follow-up Questions:

1. Are there specific integration limits that should be used here?
2. Is this problem part of a series or just a single integral evaluation?
3. Could the given result of "5" be a typographical error, or related to another constant?
4. How familiar are you with applying the power rule for integrals?
5. Is there any additional information in the problem setup not shown in the image?

Tip:

When solving definite integrals, always double-check the limits of integration before applying the result!