integral of indicator function

Hello,

I need to write matlab code for below integral. I know how to write it in discrete time but couldn't write it in integral form. Do i mutlipy the discrete form with ds and then apply the cumsum? If you help me, I appreciate it. By the way, 1_{Xs=ai} is a indicator function which is 1 when Xs=ai, otherwise 0.

Thanks in advance.

X_t=(0,1,0,1,2,1,0,...)

a_i=(0,1,2)

Y_t=int_0^t(1_{Xs=ai}ds)