If \( y=\int_{u(x)}^{v(x)} f(t) d t \), let us define \( \frac{d y}...

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If \( y=\int_{u(x)}^{v(x)} f(t) d t \), let us define \( \frac{d y}{d x} \) in a different manner as \( \frac{d y}{d x}=v^{\prime}(x) f^{2}(v(x))-u^{\prime}(x) f^{2}(u(x)) \) and the equation of the tangent at \( (a, b) \) as \( y-b=\left(\frac{d y}{d x}\right)_{(a, b)}(x-a) \)
If \( y=\int_{x}^{x^{2}} t^{2} d t \), then equation of tangent at \( x=1 \) is
(A) \( y=x+1 \)
(B) \( x+y=1 \)
(C) \( y=x-1 \)
(D) \( y=x \)
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