Edit: As has been noted in the other answers, the standard actually guarantees that "the resulting value is the least unsigned integer congruent to the source integer (modulo 2n where n is the number of bits used to represent the unsigned type)". So even if your platform did not store signed ints as two's complement, the behavior would be the same.
Apparently your signed integer -62 is stored in two's complement (Wikipedia) on your platform:
62 as a 32-bit integer written in binary is
0000 0000 0000 0000 0000 0000 0011 1110
To compute the two's complement (for storing -62), first invert all the bits
1111 1111 1111 1111 1111 1111 1100 0001
then add one
1111 1111 1111 1111 1111 1111 1100 0010
And if you interpret this as an unsigned 32-bit integer (as your computer will do if you cast it), you'll end up with 4294967234 :-)