How to get Step Response from an Impulse Response in Simulink? Im sorry if it seems like a trivial question but I am confused right now. Im currently watching my professors lecture. And he basically has $\lambda(t)$ as Step response and $k(t)$ as Impulse response of an LTI system. The integral of the Impulse response gives us the Step response:
$$ \lambda(t) = \int^{t}_{0} k(t) dt $$
and
$$ k(t) = \lambda^{\prime}(t) $$
So to see it in action I decided to make a Simulink model of that and here it is (at least I think its good if not please tell me how to do it right):

As you can see those plots are not identical but I was expecting them to be (?)
Why is that?
Your system H(s) is continuous

$$ H(s) = \frac{s}{s+1} $$

Using a discrete impulse does not make a lot of sense. I suspect Simulink added a "zero-order hold" or ZOH block between your discrete impulse and your system $H(s)$. As such, your impulse response will be affected by the sampling period of your discrete impulse source. If you decrease the sampling period, the second curve shoud match the step response more closely, although they will never be exactly the same.

Edit : 

Decrease the width of your impulse to say 0.1 second and increase the amplitude to 10 so that the area under the curve stays 1.