## How to compute the line integral of \int_{C^+}(x^2-y)dx+(y^2+x)dy?

I need help with this problem:

Compute the line integral$$\int_{C^+}(x^2-y)dx+(y^2+x)dy$$ where $$C^+$$ is the parabollic arc $$y=x^2+1$$, $$0\leq x\leq 1$$ oriented from $$(0,1)$$ to $$(1,2)$$.

First I parametrized the arc $$C^+$$ by setting $$x=t$$, then $$y=t^2+1$$, so the parametrization would be $$\alpha(t)=(t,t^2+1), t\in[0,1]$$. then I tried to solve this by using the formula $$\int_Cfds=\int_\alpha fds=\int_{0}^1f(\alpha(t))\Vert\alpha'(t)\Vert dt+\int_1^2 f(\alpha(t))\Vert\alpha'(t)\Vert dt$$. But I don’t know how to compute that, since I have an integral with respect to $$x$$ and one with respect to $$y$$.