Integration and Accumulation of Change

Evaluate the definite integral $\int_{2}^{2} (x^2 + 3x - 1) , dx$.

Given that $\int_{2}^{5} f(x) , dx = 7$, find the value of $\int_{5}^{2} f(x) , dx$.

If $\int_{2}^{6} f(x) , dx = 8$, then what is the value of $\int_{2}^{6} 5f(x) , dx$?

Given $\int_{0}^{2} f(x) , dx = 3$ and $\int_{0}^{2} g(x) , dx = -1$, find $\int_{0}^{2} [f(x) + g(x)] , dx$.

Given $\int_{0}^{5} f(x) , dx = 10$ and $\int_{0}^{2} f(x) , dx = 3$, find the value of $\int_{2}^{5} f(x) , dx$.

Given $\int_{0}^{4} f(x) , dx = 5$, find $\int_{4}^{0} f(x) , dx$.

Given $\int_{1}^{3} f(x) , dx = 4$ and $\int_{3}^{6} f(x) , dx = 7$, find the value of $\int_{1}^{6} f(x) , dx$.

Given that $\int_{1}^{5} f(x) , dx = 10$, find the value of $\int_{1}^{5} 3f(x) , dx$.

If $\int_{1}^{4} f(x) , dx = 5$ and $\int_{1}^{7} f(x) , dx = 12$, find $\int_{4}^{7} f(x) , dx$.

If $\int_{1}^{3} f(x) , dx = 4$, what is the value of $\int_{3}^{1} f(x) , dx$?