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.