1. **State the problem:** Evaluate the integral $$\int \frac{x^3 + 4}{x^2} \, dx.$$\n\n2. **Rewrite the integrand:** Simplify the expression inside the integral by dividing each term by $x^2$:\n$$\frac{x^3}{x^2} + \frac{4}{x^2} = x + 4x^{-2}.$$\n\n3. **Integral formula:** Recall the power rule for integration: $$\int x^n \, dx = \frac{x^{n+1}}{n+1} + C, \quad n \neq -1.$$\n\n4. **Apply the integral:** Integrate term-by-term:\n$$\int x \, dx = \frac{x^{1+1}}{1+1} = \frac{x^2}{2},$$\n$$\int 4x^{-2} \, dx = 4 \int x^{-2} \, dx = 4 \cdot \frac{x^{-2+1}}{-2+1} = 4 \cdot \frac{x^{-1}}{-1} = -4x^{-1} = -\frac{4}{x}.$$\n\n5. **Combine results:**\n$$\int \frac{x^3 + 4}{x^2} \, dx = \frac{x^2}{2} - \frac{4}{x} + C.$$\n\n6. **Answer choice:** This matches options (A) and (D), which are identical. So the answer is:\n$$\boxed{\frac{1}{2} x^2 - \frac{4}{x} + C}.$$