The value of $\int_1^a[x] f^{\prime}(x) d x, a>1$, where $[x]$ denotes the greatest integer not exceeding…

The value of $\int_1^a[x] f^{\prime}(x) d x, a>1$, where $[x]$ denotes the greatest integer not exceeding $x$ is
  1. $\operatorname{af}(a)-\{f(1)+f(2)+\ldots+f([a])\}$
  2. $[a] f(a)-\{f(1)+f(2)+\ldots+f([a])\}$
  3. $[a] f([a])-\{f(1)+f(2)+\ldots+f(a)\}$
  4. $a f([a])-\{f(1)+f(2)+\ldots+f(a)\}$

Asked in: JEE Main 2006

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