Answer:
a. (-pi/2, pi/2)
b. (-pi, pi/2) U (pi/2, pi)
c. -pi/2
d. pi/2
Explanation:
g'(x)=cos(t) (-pi,pi) Fundamental Theorem of Calculus
It increases while g'(x) is positive, so (-pi/2, pi/2)
It decreases while g'(x) is negative so (-pi, pi/2) U (pi/2, pi)
The local minimum occurs when g'(x) switches from negative to positive
The local maximum occurs when g'(x) switches from positive to negative