Evaluating a polynomial definite integral via FTC Part 2

First find an antiderivative of each term. Since $\int 5x^4\,dx = x^5$, $\int 3x^2\,dx = x^3$, and $\int 2\,dx = 2x$, an antiderivative of the integrand is $F(x) = x^5 - x^3 + 2x$. By FTC Part 2, $\int_1^2 (5x^4-3x^2+2)\,dx = F(x)\Big|_1^2 = F(2) - F(1)$.

Now evaluate: $F(2) = 2^5 - 2^3 + 2(2) = 32 - 8 + 4 = 28$, and $F(1) = 1^5 - 1^3 + 2(1) = 1 - 1 + 2 = 2$. Therefore the integral equals $F(2) - F(1) = 28 - 2 = 26$.