# Python 2,  <s>83</s> 78 bytes

this version saved 10 bytes, thanks to @numbermaniac :

    x=input()
    print len(''.join(map(str,(range(x+1)if x>0 else range(0,x-1,-1)))))

this one I came up with on my own after that (same amount of bytes):

    x=input()
    print sum(map(len,map(str,(range(x+1)if x>0 else range(0,x-1,-1)))))