Find the laplace transform of the piecewise function ft1 if

Find the laplace transform of the piecewise function.
f(t)={1, if 0<=t<4
        {2, if t>=4
I\'m confused on this one so a step by step would be very nice.

Solution

f(t) = 1( u(t) - u(t - 4) ) + 2( u(t - 4) )

where u(t) = Unitstep Function

L[ u(t - a) ] = ( e^-as/s )

The Heaviside step function, or the unit step function, usually denoted by (but sometimes u), is a discontinuous function whose value is zero for negative argument and one for positive argument. It is an example of the general class of step functions, all of which can be represented as linear combinations of translations of this one.

The function was originally developed in operational calculus for the solution of differential equations, where it represents a signal that switches on at a specified time and stays switched on indefinitely. Oliver Heaviside, who developed the operational calculus as a tool in the analysis of telegraphic communications, represented the function as 1.

Now taking Laplace of the above formed function .

L[ f(t) ] = (1/s) - (e^-4s/s) + 2(e^-4s/s) = ( 1 + e^-4s )/s