A) \[\int_{0}^{1}{f(x)\,dx}\]
B) \[\int_{0}^{1}{f(-x)\,dx}\]
C) \[\int_{0}^{1}{f(x-1)\,dx}\]
D) \[\int_{-1}^{1}{f(x)\,dx}\]
Correct Answer: A
Solution :
Put \[1-x=t\Rightarrow -dx=dt\]. Also as \[x=0\]to 1, \[t=1\]to 0 Therefore, \[\int_{0}^{1}{f(1-x)dx=\int_{1}^{0}{f(t)(-dt)}}=\int_{0}^{1}{f(t)dt=\int_{0}^{1}{f(x)dx}}\].
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