Three Unknowns in One Line?

Calculus Level 4

The equation limx00xt2dt(xsinx)a+t=1 \displaystyle \lim_{x \to 0} \int_0^x \frac {t^2 \mathrm d t}{(x- \sin x) \sqrt{a+t} } = 1 is true for a constant aa.

What is the value of a?a?

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