Find $\int_1^3f(x)\ dx$ if $\int_0^1f(x)\ dx$ , $\int_0^4f(x)\ dx$ and $\int_3^4f(x)\ dx$ are given Say I have some integrals:
$$\int_0^1f(x)\ dx=3$$
$$\int_0^4f(x)\ dx=-5$$
$$\int_3^4f(x)\ dx=1$$
How exactly do I go about evaluating the integral for:
$$\int_1^3f(x)\ dx$$
My idea is I must take the area of each individual segment and add them together. Or average. I am lost here.

Sketch a diagram and convince yourself this must indeed be the case:
$$\int_0^4 = \int_0^1 + \int_1^3 + \int_3^4$$
