The function F is twice differentiable for all real numbers, and its derivative is given by
F′(t)=e2t−sint.
It is known that F(0)=3.
(a) Express F(x) in terms of a definite integral whose lower limit is 0 and upper limit is the variable x. Clearly indicate all quantities of integration.
(b) Calculate the exact value of F(1). Show all steps of your computation, including the evaluation of any integrals and arithmetic simplifications.