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Given $\int_{-\infty }^{\infty } e^{-x^{2}} dx = \sqrt{\pi }.$

If $a$ and $b$ are positive integers, the value of $\int_{-\infty }^{\infty } e^{-a\left ( x+b \right )^{2}} dx$ is _______________.

  1. $\sqrt{\pi a}$
  1. $\sqrt{\frac{\pi }{a}}$
  1. $b\sqrt{\pi a}$
  1. $b\sqrt{\frac{\pi }{a}}$
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