Question

Please help with a Calculus Integral question!
It requires mathtype so give me a second. :)

Answer 1

If \[\int\limits_{2}^{5} f(x)dx = 4 \]
and \[\int\limits_{2}^{7} f(x) = -3 \]
then what is \[\int\limits_{7}^{5} f(x)dx \]

Answer 2

I'm not really sure how to start, I think I am confused because the integral in the middle is f(x) and not f(x)dx like the other two, does that mean anything?
Anyway, I know that from 7 to 5 is going to be negative, but that's pretty much all I can figure out right now.
The problem is multiple choice, but I usually like to solve it before looking at the answers as it is best to be confident in one's solution.
Help is appreciated!

Answer 3

I got positive 7 as my answer? Can anyone tell me if I am correct? I theorized that because 2 to 7 is 5 spaces and 2 to 5 is three spaces, I needed two spaces for 7 to 5, so I did this:
-3 -4 = -7
-(-7)= 7 because it is a backwards interval
Sound good? o. o