Chapter 4: Applications of Derivatives - Section 4.7 - Antiderivatives - Exercises 4.7 - Page 238: 19

$t^3+\dfrac{t^2}{4}+C$

Since, we have $\int (3t^2+\dfrac{t}{2}) dt=t^3+\dfrac{t^2}{4}+C$ and $\dfrac{d}{dt}(t^3+\dfrac{t^2}{4}+C)=3t^2+\dfrac{t}{2}$ Thus, the derivative of the integral is integrand. So, the answer is correct.