f(x)g(x-t)dt Integrating over t can be visualized as sliding g over f over the range of t. Result is a function of x as t has been integrated out. It all made

f(x)g(x-t)dt Integrating over t can be visualized as sliding g over f over the range of t. Result is a function of x as t has been integrated out. It all made sense to me when I thought of it as sliding one function over another fixed function.