A chemist records the rate of consumption of a reactant at time t hours by the function R(t)=2t2−3t+4sint (in grams per hour).
(i) Write an integral expression for the total amount of reactant consumed from t=0 to t=π hours.
(ii) Determine an antiderivative F(t) of R(t).
(iii) Hence calculate the exact total amount of reactant consumed in that time interval.