If function f(x) is continuous in the interval (a, b) and having same definition between a and b, then we can find `int _(a) ^(b) f (x) dx if f (x)` is discontiuous and not same definition between a and b, then we must break the interval such that f(x) becomes continuous and having same definition in the breaking intervals.
Now, if f (x) is discontinuous `at x =c (a lt c lt b),` then `int _(a)^(b) f (x) dx = int _(a)^(c ) f (x) dx + int _(c ) ^(b) f (x) dx and ` also if f (x) is discontinous at `x =a` in `(0, 2a),` then we can write `int _(0) ^(2a) f(x) dx = int _(0) ^(a ) {f (a-x) + f(a+x) } dx`
On the basis of above information, answere the following questions :
`int _(-1)^(1) [|x|] d ((1)/(1+ e ^(-1//x)))` (where `[.]` denotes the greatest integer functions ) is equal to

Options

A. `-3`
B. `-2`
C. `-1`
D. None of these

Answer

D