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How would you go about integrating this?

$ \int_{-\infty}^{\infty} \, e^{-ax^2} e^{-b(c-x^2)} dx$

Where a,b,c are constants.

Don't really know where to begin

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    Write your integrand function as $e^{-bc} e^{-(a-b)x^2}$. – 2017-02-24
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    And if $a-b>0$, change variables to get an integral of $e^{-t^2}$ – 2017-02-24
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    Oh my. Not one, not two, but three useless parameters! – 2017-02-24

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$\displaystyle I=\dfrac{e^{-bc}}{\sqrt{a-b}}\int_{-\infty}^\infty e^{-x^2}\; dx=\dfrac{e^{-bc}\sqrt{\pi}}{\sqrt{a-b}}$

The integral holds only if $a\gt b$ .