If f is continuous for all x, which of the following integrals necessarily have the same value?

B

Step-by-step explanation:

Given the three integrals, we want to determine which integrals necessarily have the same value.

We can let the first integral be itself.

For the second integral, we can perform a u-substitution. Let u = x + a. Then:

Changing our limits of integration:

Thus, the second integral becomes:

For the third integral, we can also perform a u-substitution. Let u = x + c. Then:

And changing our limits of integration:

Thus, our third integral becomes:

Since the only difference between f(x) and f(u) is the variable and both the first and third integral have the same limits of integration, our answer is B.