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Given that $f''(x)=2$, $f'(2)=5$, and $f(2)=10$, find the function $f(x)$.

$f(x)=2x+1$

$f(x)=x^{2}+x$

$f(x)=x^{2}+6$

$f(x)=x^{2}+x+4$