Dirac Delta Function Integral

Hi.

Im having some trouble with the following question:

"Evaluate the integral: **e^x [dirac(x + 1) − dirac(x − 2)] dx **from -ve infinity to 1"

Am i supposed to use a Laplace transformation? In which case I split it into 2 integrals:

**e^x * dirac(x + 1) **

minus....

**e^x * ****dirac(x − 2) dx**

So for the first integral I get exp(p-1), and for the second exp(2-2p). So overall exp(p-1) - exp(2-2p).

However as the original integral was from -ve infinity to 1, the second dirac integral (at x=2) would be out of this boundary. So would I disregard this?

Have I gone about this problem in the correct way?

Thanks in advance.