Numerically Integrate two vector values to produce a vector output.

I have two vectors a, and t. I need a vector answer c.
c(T) = integral of a(b) with respect to t (dt), between T and 0.
And i need c(T) to be in vector form. I've tried trapz, but this obly gives me a single value. And i cant use the 'quad', or 'intergral' function, as i do not have an imput function. (Or cannot figure out how to create a function for this that works).
I am getting my a, and t, values from another function.
Help please.

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can you provide some sample code to set up a small-scale version of your problem? I'm having trouble understanding how (i.e. in what context) the output of an integration could/should be a vector.

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