laplace(syms) leads to incorrect answer?

This code nicely demonstrates my confusion:

syms t real
f=heaviside(t+1)
laplace(f)
f=heaviside(t-1)
laplace(f)

Producing the output:

f =

heaviside(t + 1)

ans =

1/s

f =

heaviside(t - 1)

ans =

exp(-s)/s

The first laplace should return exp(s)/s, yet matlab transforms as if there is not time shift?

[David Wilson]

Might be somethng to do with the one-sided or two-sided definitions of the Laplace transform.

[Walter Roberson]

Maple agrees with MATLAB