Gaussian integral 2016, Part II

Calculus Level 4

The Gaussian integral states that \( \displaystyle \int_{-\infty}^{+\infty} e^{-x^2 } \, dx = \sqrt{\pi } \).

Hence or otherwise, evaluate the integral

\[ \displaystyle \int_{-\infty}^{+\infty} e^{-x^2 + 2x + 2016} \, dx \]

If the above integral can be expressed in the form \( a e^{b} \sqrt{\pi} \), where \(a , b\) are positive integers, find \( a+b\).

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