If `f '(x) = 3x ^(2) + 2x` then by definition of Integration, we get `f (x) = x ^(3) + x ^(2) + c`

Answer

To solve the problem, we need to integrate the function \( f'(x) = 3x^2 + 2x \) to find \( f(x) \).

### Step-by-Step Solution:

1. **Identify the function to integrate**:
We have \( f'(x) = 3x^2 + 2x \).

2. **Set up the integral**:
We need to integrate \( f'(x) \):
\[ f(x) = \int (3x^2 + 2x) \, dx \]

3. **Integrate each term separately**:
- The integral of \( 3x^2 \):
\[ \int 3x^2 \, dx = 3 \cdot \frac{x^{2+1}}{2+1} = 3 \cdot \frac{x^3}{3} = x^3 \]
- The integral of \( 2x \):
\[ \int 2x \, dx = 2 \cdot \frac{x^{1+1}}{1+1} = 2 \cdot \frac{x^2}{2} = x^2 \]

4. **Combine the results**:
Now, we can combine the results of the integrals:
\[ f(x) = x^3 + x^2 + C \]
where \( C \) is the constant of integration.

5. **Conclusion**:
Therefore, we conclude that:
\[ f(x) = x^3 + x^2 + C \]
The statement given in the question is true.