Hint: Remember that Integral [a,b] + Integral [b,c] = Integral[a,c] where a < b < c. Try using this and re-arranging to get the answers to these questions.
If you know f(x) is continuous, even and: f(t)dt=2 on the integral 0 to 2, f(t)dt=-1 on the integral 1 to 2, and f(t)dt=7 on the integral 2 to 4:
What is f(t)dt on the integral -1 to 2
What is f(t-1)dt on the integral 1 to 2
and what is the average value of f(x) on the interval [-4,4]
Thank you so much!