Finding impulse of a CT system

[asd1249jf]

Homework Statement

A continuous-time system has the input/output relationship

$$y(t) = \int_{-\infty}^{t} (t - \lambda + 2)x(\lambda) d\lambda$$

Determine the impulse response h(t) of the system

Homework Equations

Convolution theorems

$$y(t) = x(t) * h(t)$$
Where y(t) is the output, x(t) is the input and h(t) is the impulse response

The Attempt at a Solution

I have absolutely no clue how to obtain the impulse response, going backwards in a CT domain from the given equation above. Can anyone give me some hints to start me off?

 

[doodle]

Express the convolution as an integral. Compare this integral with the problem statement and obtain a function of the form $h(t-\lambda)$. It should not be too difficult then to determine $h(t)$.