Question about changing an integral bounds due to a reflection.
Suppose you have an integral across $\Bbb R^{+}$ such that $$I=\int_{0}^\infty f(t)dt$$ Would $I$ be the same if I applied a reflection across the y-axis such that $t\to-t$ and integrated along $\Bbb R^{-}$ such that$$I=\int_{-\infty}^0 f(-t)dt$$ Is this ok?