Concept:Use substitution in a definite integral to change both the variable and the limits.Explanation:Let t=x+6.Then dt=dx.When x=a−6, t=(a−6)+6=a.When x=b−6, t=(b−6)+6=b.So ∫a−6b−6​f(x+6)dx=∫ab​f(t)dt.The variable of integration is arbitrary in a definite integral, so ∫ab​f(t)dt=∫ab​f(x)dx.Hence ∫a−6b−6​f(x+6)dx=∫ab​f(x)dx.Answer:∫a−6b−6​f(x+6)dx=∫ab​f(x)dx, which is Option C.