Answer
$\dfrac{t^3}{6}+t^4+C$
Work Step by Step
Since, we have $\int (\dfrac{t^2}{2}+4t^3) dt=\dfrac{t^3}{6}+t^4+C$
Also, $\dfrac{d}{dt}(\dfrac{t^3}{6}+t^4+C)=\dfrac{t^2}{2}+4t^3$
Thus, the derivative of the integral is integrand. So, the answer is correct.