If \int\limits^a_b {f(x)} \, dx = 5 and \int\limits^a_c {f(x)} \, dx = 0. What is the value of \int\limits^b_c {f(x)} \, dx = ..?

Question

If
`\int\limits^a_b {f(x)} \, dx = 5` and
`\int\limits^a_c {f(x)} \, dx = 0`.

What is the value of
`\int\limits^b_c {f(x)} \, dx = ..?`

Answer 1

`\boxed{\int\limits^b_c {f(x)} \, dx = -5}`

.

Explanation:

`\int\limits^a_c {f(x)} \, dx + \int\limits^b_a {f(x)} \, dx = 0 + (-5)`

`\int\limits^b_c {f(x)} \, dx = -5`