A vertical rectangular surface has height $H$ and spans $x=0$ to $x=a$. A magnetic field $B\left(x\right)$ points horizontally through the surface, making a constant angle $\theta$ with the outward area vector. Which expression correctly represents the flux?

${\Phi }_B={\int }_0^{H}B\left(x\right)a\cos \theta dx$

${\Phi }_B={\int }_0^{a}B\left(x\right)H\sin \theta dx$

${\Phi }_B=B\left(a\right)Hacos\theta$

${\Phi }_B={\int }_0^{a}B\left(x\right)H\cos \theta dx$