The value of \( \lim _{x \rightarrow 1^{+}} \frac{\int_{1}^{x}|t-1| d t}{\sin (x-1)} \) is (a) 0...

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The value of \( \lim _{x \rightarrow 1^{+}} \frac{\int_{1}^{x}|t-1| d t}{\sin (x-1)} \) is
(a) 0
(b) 1
(c) Doesn't exist
(d) None of these
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