Question

if u = -x and du = -dx, why is integral -b to -a f(u)du = integral -b to -a f(x)dx ?

Answer 1

Well I think you only can do this:
\[\displaystyle\int_{-b}^{-a}f(u)du=-\displaystyle\int_{b}^{a}f(-x)dx\\(u=-x\longrightarrow du=-dx)\]