Can Variable Substitution Validate This Integral Transformation?

[machinarium]

I forgot all about integral so I need some help from you.
\int\stackrel{0}{-a}x(t)dt=\int\stackrel{0}{a}x(t)d(-t)=\int\stackrel{0}{a}x(t)(-dt)

Please explain it to me. I want to transform \int\stackrel{0}{-a}x(t)d(t) to \int\stackrel{a}{0}x(-t)d(t) but don't know how.

 

[LCKurtz]

I forgot all about integral so I need some help from you.
\int\stackrel{0}{-a}x(t)dt=\int\stackrel{0}{a}x(t)d(-t)=\int\stackrel{0}{a}x(t)(-dt)

Please explain it to me. I want to transform \int\stackrel{0}{-a}x(t)d(t) to \int\stackrel{a}{0}x(-t)d(t) but don't know how.

Use the substitution u = -t, du = - dt in both the integrand and the limits.