Answer
$0$
Work Step by Step
$$\eqalign{
& \int_5^5 {\left( {{t^2} + \sin t} \right)} dt \cr
& {\text{Using the property of integrals }}\int_a^a {f\left( x \right)} dx = 0 \cr
& \int_5^5 {\left( {{t^2} + \sin t} \right)} dt = 0 \cr} $$