Solving Inequality System: Finding the Values of 'a' and 'b'

Translation: Solving the inequality 'x-a≥1', we get 'x≥a+1'. Solving the inequality 'x+5≤b', we get 'x≤b-5'. Since the solution set of the inequality system is '3≤x≤4', we have 'a+1=3' and 'b-5=4'. Therefore, 'a=2' and 'b=9'. Thus, 'a+b=2+9=11'. Therefore, the answer is C.