What happens if the greater limit becomes smaller when you change them for u-substitution? If I am doing u-substitution on a definite integral, and my upper limit is $b$ and my lower limit is $a$, and I change the limits to match the u, what happens if my $b$ turns out to be lower than my $a$ (so the now b is smaller than a)?
Does my new b still go at the top, or must I maintain the order?
For example, if $u = 1 + cosx$, and $b = \frac{\pi}{2}$, and $a = \frac{\pi}{3}$, when I change them, I get $b = 1$, and $a = 1.5$.
Now $a$ is greater than $b$.
So which goes at the top of the integral sign (which is the upper limit)?
$ \int_b^a u(x) dx= - \int_a^b u(x) dx.$
$ \int_b^a u(x) dx= - \int_a^b u(x) dx.$