How to write an integral using 'cumsum'?

I want to write this discretized integral in MatLab using 'cumsum'.

I tried the following (where i0 = find(x==0))

    Pp=Dx*cumsum(u(i0:end));
    Pm=-Dx*[fliplr(cumsum(fliplr(u(1:i0-1)))) 0];
    P=[Pm Pp];
    Pk=0.5*(P(1:end-1)+P(2:end));

to compute $ \int_{-1}^{1} u(y,t) dy$ (for a fixed, to be evolved later time level; the integral from -1 to 1 of the function u(x,t)dx.) Now I want to compute [integral from 0 to x of the function u(y,t)dy] - [integral from 0 to 1 integral from 0 to y of the function u(z,t)dzdy] ~ I have attached the discretized form here with.

Any kind of help regarding this coding would be much appreciated.