Question 1183694
Clearly, g(x) is given by {{{g(x) = int(f(t), dt, -4, x)}}} because of the presence of the elongated "s", the superscripted "x", and the underscored "-4".  
With this in mind, we make the following evaluations --


===> (a){{{g(-8) = int(f(t), dt, -4, -8) =  -int(0, dt, -8, -4) = 0  }}}


(b)  {{{g(-3) = int(f(t), dt, -4, -3) = int(2, dt, -4, -3) = 2*(t)[-4]^-3 = 2(-3--4) = 2*(1) = 2}}}


(c) {{{g(0) = int(f(t), dt, -4, 0) =  int(2, dt, -4, -1) + int((-5), dt, -1, 0) = 6-5 = 1}}} 


(d)  {{{g(4) = int(f(t), dt, -4, 4) = int(2, dt, -4, -1) + int((-5), dt, -1, 3) + int(0,dt, 3,4) = 6-20+0 = -14}}} 


(e) Doing the necessary piecewise integration, what we get is

{{{g(x) = system(matrix(4,2,0,x<-4,2(x+4)=6+2(x+1), -4 <=x <-1 , 6-5(x+1), -1 <= x < 3, -14, x>=3 )  ) }}}


By inspection one can see that the abs max value of g(x) occurs at {{{highlight(x = -1)}}}, with function value {{{highlight(g(-1) = 6)}}}.