Average value of a function

g[x_]:=(((x-3))^3)-(x-3)
a=2;
b=5;
Manipulate[Show[{
RegionPlot[{y≤g[x]&&y≥0||y>g[x]&&y<0,0<=y≤c},{x,a,b},{y,-2,7},PlotPoints->50],
Plot[{g[x],c},{x,2,5},PlotRange->{{2,5},{-1,7}}]},PlotRange->{{2,5},{-1,7}}],{{c,0},-1,4}]

c1=Solve[(1/((b-a)))(∫_a^b)g[x]\[DifferentialD]x==g[c] ,c][[1]][[1]][[2]]