The value of $\begin{align*} \int_1^a [x] \; f'(x) \;dx, \; a > 1 \end{align*}$, where $[x]$ denotes the greatest integer not exceeding $x$, is :

Question

( A ) $[a] f(a) - \{f(1) + f(2) + ....+ f([a])\}$
( B ) $a f([a])- \{f(1) + f(2) + ....+ f(a)\}$
( C ) $a f(a)- \{f(1) + f(2) + ....+ f([a])\}$
( D ) $[a] f([a])- \{f(1) + f(2) + ....+ f(a)\}$