设$f\left(x\right)$连续，$x\gt 0$，且${\int }_{1}^{{x}^{2}}f(t)dt={x}^{2}(1+x)$，则$f\left(2\right)=$$(\,\,\,\,\,)$
$A、$$4$
$B、$$2\sqrt {2}+12$
$C、$$1+\dfrac {3\sqrt {2}}{2}$
$D、$$12-2\sqrt{2}$
【题目】-|||-已知 (x)=(int )_(x)^2sqrt (2+{t)^2}dt 则 f(1)= () .-|||-
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