#### Answer

$\int_{-1}^{0} 2x^3 dx$

#### Work Step by Step

By using the definition of the definite integral, P is a partition of [-1,0], therefore the lower and upper limits of the integration are -1 and 0. $f(c_{k})=2c_{k}^3$ is the function in the additive of the Riemann sums, therefore $f(x)=2x^3$. Therefore the solution is: $\int_{-1}^{0} 2x^3 dx$.