please state which option is correct with an explanation , thanks..

Use the Taylor series for e- to evaluate 1 the integral 1. I = 3 . 22k K! k=0 I = Be- dx. (-1)k 2. I = 3 . 22k- k=0 k! 1 3. I = M: 3 .22k-+1 *=0 k!(2k + 1) O (-1)k 4. 1 = 3 . 22k-+1 2k + 1 k=0 (-1) k 5. 1 = M 3. 22k+1 k!(2k + 1) k=0\fFind the Taylor series centered at the origin for the function f(a:] = $005 (53) .