Find the value of `[1/2]+[1/2+1/1000]+ *[1/2+2946/1000]` where [.] denote greatest integer function ?

The value of int_(-2)^1 [x[1+cos((pix)/2)]+1] dx, where [.] denotes greatest integer function is

The sum of [1/2]+[1/2+1/(2000)]+[1/2+2/(2000)]+[1/2+3/(2000)]++[1/2+(1999)/(2000)] where [.] denote the greatest integer function, is equal to: 1000 (b) 999 (c) 1001 (d) none of these

The sum of [1/2]+[1/2+1/(2000)]+[1/2+2/(2000)]+[1/2+3/(2000)]++[1/2+(1999)/(2000)] where [.] denote the greatest integer function, is equal to: 1000 (b) 999 (c) 1001 (d) none of these

The sum of [1/2]+[1/2+1/(2000)]+[1/2+2/(2000)]+[1/2+3/(2000)]++[1/2+(1999)/(2000)] where [.] denote the greatest integer function, is equal to: 1000 (b) 999 (c) 1001 (d) none of these

[(4)/(5)] + [(4)/(5)+(1)/(1000)] + [(4)/(5)+(2)/(1000)] + ...+[(4)/(5) + (999)/(1000)] = where [.] denotes greatest integer function

[(4)/(5)] + [(4)/(5)+(1)/(1000)] + [(4)/(5)+(2)/(1000)] + ...+[(4)/(5) + (999)/(1000)] = where [.] denotes greatest integer function

The value of int_(-g)^(1)[x[1+cos((pi x)/(2))]+1]dx where [.] denotes greatest integer function is

The value of int_(-pi//2)^(pi//2)[ cot^(-1)x] dx (where ,[.] denotes greatest integer function) is equal to

The value of int_(-pi//2)^(pi//2)[ cot^(-1)x] dx (where ,[.] denotes greatest integer function) is equal to