No, you can't! s(x-a) is equal to 0 from negative infinity to a, 1 from a to infinity.
which does not exist.
but I mean by this step function that it is equall one in the region from zero to a, and it is equall zero in all the regions less than zero and greater than a, so I quessed that its integration from zero to infinity will be reduced to the interval where it is equall one (from zero to a). I thought of it as a multiplication by zero (which gives zero) in all regions except when x goes from zero to a.